Best Of

Sam, might have been is a FORM, not a PART OF SPEECH.

Yes, might is best described as a MODAL AUXILIARY VERB or, more simply, a MODAL VERB.
This is what could be termed a PART OF SPEECH, though I prefer the term WORD CLASS.

It's debatable whether may and might should be seen as two Modal Verbs or two FORMS (PRESENT AND PAST) of the same verb. Either way, might have been is a PERFECT FORM.

Personally, I tend to think of might have been as a MODAL PAST PERFECT of be.
An important book on the English Verb by FR Palmer uses the term SECONDARY rather than MODAL.
From this point of view
PRIMARY had been
corresponds to
SECONDARY might have been/could have been/would have been/should have been.
Had been is unquestionably PAST PERFECT, so I prefer to think of might have been etc as also PAST PERFECT, but there's clearly a contrary argument which does not recognise it as a PAST form.

In my speech and for many other speakers — though perhaps not for everybody

• may have been means 'was perhaps, I don't know but it's a possibility'
• might have been can have at least these meanings:
  —1. 'was perhaps, I'm not really sure'
  —2. 'had been previously perhaps, I'm not really sure'
  —3. 'wasn't, as it happens, but if conditions had been different could have been'
  —4. 'hadn't been previously, as it happens, but if conditions had been different could have been'
  Some speakers, not me, can use may have been for meaning [3].

My meaning [1] would support 'I don't really know what Stone Age houses were like, but this is a possibility'.
My meaning [3] would support 'If there had been Stone Age houses, they would have been like this'.

As with modal verbs in general, the modality — in this case POSSIBILITY (technically epistemic modality) — may be attached to different aspects of the proposition.

• PRESENT JUDGEMENT OF POSSIBILITY ABOUT THE PAST — e.g._ may have been, might have been, will have been, would have been_
  This would cover your meaning (i) — a present judgement that it's possible, though dubious, that a Stone Age house like this existed

• JUDGEMENT OF POSSIBILITY AT THE TIME (IN THE PAST) — e.g. might have been, could have been, would have been, should have been but not_ may have been, can have been, will have been, shall have been_
  This would cover your meaning (ii) — judgement that this represents a possible design for a house in the Stone Age.

We were busy studying is clearly a blend of we were busy and we were studying. WE understand the blend, so logically we must understand the structure.

That leaves the problem of attaching labels to individual bits. It's a question of terminology, not fact.

Unfortunately, traditional grammar has left us with a mixture of useful and less useful terms. And these terms are only partly sufficient for describing the structure of a language like English.

• busy can indeed be termed an ADJECTIVE. Any grammatical description of English, traditional or modern, would use the term.
  And many grammars would use the term COMPLEMENT.

• studying is not so easy.
  I very much prefer to use the term -ing FORM. Traditional grammars use the terms PARTICIPLE and GERUND. They are perhaps useful for a good many clear-cut instances, but they are inadequate for others. All we can say of _studying in this sentence is that it can't be called a gerund. If you find it helpful to call it a participle, go ahead.

• eaten can't possibly be termed a gerund.
  In any grammar of English, this term is exclusively used for -ing forms of verbs.
  (Actually in grammars of Old English, the term is used for a very different form, but English grammar has changed radically since then.)
  The traditional term PARTICIPLE is used in pretty well all grammars.
  More specifically, traditional grammars use the term PAST PARTICIPLE. There are good historical reasons for this, but it is slightly confusing. This verb form is often PASSIVE in meaning. And it's used to form PRESENT PERFECT as well.
  Unfortunately, we cant simply term it an -ed FORM. Words like eaten have -en instead of -ed. Words like drunk don't have a suffix. And an -ed form is also used for PART SIMPLE.
  Some grammars use terms like -ed2 or third form.
  Whatever term you use, the same verb form is used in three ways in English
  — 1. with PASSIVE meaning — used like an ADJECTIVE
  — 2. to form PASSIVE verb forms — after what you term a LINKING VERB
  — 3. to form PERFECT verb forms — generally after have

• being is another -ing form which can't possibly be termed a gerund.
  The facts are that
  — -ing forms are used to form PROGRESSIVE verb forms
  — forms of be (and other linking verbs are used with forms like eaten to form PASSIVE verb forms
  — being (and -ing forms of other linking verbs) is used with forms like eaten to form PASSIVE PROGRESSIVE forms
  You can used whatever term you find useful. Some grammars would call being a participle.

I'll try to answer your question about helping vers and linking verbs in another post.

also, are linking verbs ever used with helping verbs?

• helping verb is a term that a few grammars use in place of the traditional AUXILIARY.
  There are two classes of auxiliary in English
  —1. PRIMARY AUXILIARY — be, have, do
  —2. MODAL AUXILIARY (or SECONDARY AUXILIARY) — can, could, will, would, may, might, must, shall, should

• linking verb is a term for verbs like be, become, seem, sound etc
  Their grammatical characteristic tic is that
  — a following NOUN PHRASE refers to the same thing as the SUBJECT
  — a following ADJECTIVE is a description of the SUBJECT
  This use may be termed PREDICATIVE ADJECTIVE, as opposed to an ATTRIBUTIVE ADJECTIVE before a NOUN.

So be can be a linking verb or a 'helping verb' or both — as in is being eaten

Other possible combinations are

• have + be — has been eating, has been eaten
• can + be — can be eating, can be eaten
• can + have +be + — can have been eaten
• can + seem — can seem nice

There's a problem of terminology with have and do. They are also used in a different sense and with a different grammar.

• in is having a shower, have is not an auxiliary (helping verb),
• in is doing her homework, do is not an auxiliary (helping verb)

Another terminological problem with do is that is used in two ways as an auxiliary:
—1. before a verb which isn't an auxiliary (aka a LEXICAL VERB) — does eat, didn't eat
—2. instead of a lexical verb and the words after it — Alice doesn't eat it but I do
In this second use, we sometimes use do after another auxiliary — I have done, I am doing.
BUT NOT
in the first use — I have done eaten, I am doing eating
The possibilities of combining do with another auxiliary are limited.
And so are combinations with a linking verb.
I think the only possibility is when do is used for emphasis or negation, and where it is before the linking verb. — do be nice, don't sound angry, it doesn't seem right.

It's not usual to have be before a different linking verb, because these verbs are not usually used in PROGRESSIVE forms. However, we can use them to express temporary meaning, so we can say, for example — It's now seeming more likely.

For all these questions of combining verb forms, a good grammar must

FIRST describe the facts — what combinations of forms are possible or impossible

THEN choose grammatical terms which are helpful and not confusing

It isn't a tense, @Ritsu.

You've been misled by the term PAST PARTICIPLE. That verb form could just as well be called a PASSIVE PARTICIPLE.

There's nothing unusual in using this form as an ADJECTIVE. Think of

known, increased, damaged, closed, fried, depressed ...

Dedicated passes all the tests for recognising a word as an adjective.

1. It can be used before a noun — e.g. a dedicated doctor
2. It can be used after be — e.g. She's dedicated
3. It can be used with very — e.g. They're very dedicated
4. It can be used comparatively — e.g. She's more dedicated than you

The first problem to tackle is articles — frequently a nightmare for Russians speaking of writing English. Because of the phrase of the Russian Federation development you must write

the strategic goals.

That's probably my only grammatical objection, but there are other things that could be improved.

You seem to be writing about goals of development — adding as extra information strategic and of the Russian federation. I think it would be better if you change to development goals. Thus:

achieving the strategic development goals of the Russian Federation

I don't see why your first clause is PASSIVE. It gives too much importance to the words is considered. Another problem with having is considered in the middle of your sentence is that it leads the reader to expect a clause with a different verb after the comma.

These problems disappear if you start with ACTIVE

This paper [or dissertation or whatever] considers the role ...

After the comma you could then write

and also the provisions...

I'm not sure why you write program rather than Program. If it's the official name of a program, then all the content-words should be capitalised. Thus

the Digital Economy of the Russian Federation Program

— although I suspect it's better described as

the Digital Economy Program of the Russian Federation

He is a boy.

• Don't you mean X? = 'I think you mean X. Am I right?'

• Do you mean X? = 'I don't know whether you mean X or not. Which is true?'

Articles are useful in making complicated sentences much clearer.

If you want to write about
1. an application
2. an approval process
then you should help the reader by using two articles.

The only time it's helpful to omit the second article is when the two noun represent a closely related pair of things such as the top and bottom, the start and finish, the mother and father. There are two problems with application and approval process

• The meaning: They're not an obvious pair
• The difference in form: One is a single noun and the other is a compound of two nouns

The other article problem was with the word loan. This is a COUNTABLE NOUN, so the grammar insists on an article or some other DETERMINER before the SINGULAR form:
a loan, the loan, this loan, that loan, my loan, your loan etc or the NUMERAL one loan

Before the plural form loans we can have no article if the meaning is INDEFINITE. Some grammar books call this the ZERO ARTICLE.

The only other use of a ZERO ARTICLE is when the noun is UNCOUNTABLE.

Home-construction is an example. Although the simple noun construction can be COUNTABLE (one construction, two constructions etc) it can also be ABSTRACT and grammatically UNCOUNTABLE. The compound home-construction could possibly be used to mean 'one example of a home being built' but this would be unusual and possibly confusing. It normally refers to the ABSTRACT concept of constructing homes, so we would say
a loan for home-construction
not
a loan for a home-construction.

Approval is another noun that is UNCOUNTABLE in the sense that you're using it — in the phrase approval process. This can be rephrased as
the process of approval
not
the process of an approval.

The first won't do, but Farcical Tales is a possible phrase.

There's a difference between farce and a farce, so you must decide which you mean,

A farce (PLURAL farces) is a comic play of a particular type .

You can also use a farce to mean 'a situation which is like a farce'.

[I don't think I'd use the PLURAL farces to mean 'situations which are like farces']

Farce (no PLURAL) is the genre, that is to say the type of comedy.

I suggest you look carefully at the examples for meanings 1, 1.1 and 1.2 here:

https://en.oxforddictionaries.com/definition/farce

An important question is whether you are discussing a variety of plays (or situations) or just one.

The only justification for Tales of a Farce is if there are several stories concerning one play (or situation)

'Monday's, Tuesday's and Wednesday's meetings were cancelled.' is more logical.

Strictly speaking 'Monday, Tuesday and Wednesday's meetings were cancelled.' states that Monday was cancelled, Tuesday was cancelled and Wednesday's meetings were cancelled. However, nobody would assume that you meant to say this.

Personally I would prefer to say
'Monday's, Tuesday's and Wednesday's meetings were all cancelled.'
or
All meetings were cancelled for Monday, Tuesday and Wednesday.

Normally, I would mark with possessive -'s each possessor in a chain linked by and — with these exceptions
1. One possession is shared e.g. John and Mary's house
2. The possessors constitute a group e.g. the King and Queen's various attendants, Oxford and Cambridge's Colleges,

In writing, I would avoid possessive -'s forms for non-human possessors e.g. the meetings on Monday, Tuesday and Wednessday, the Colleges of Oxford and Cambridge

Monday, Tuesday and Wednesday is just a list of days — no more a group than Saturday, Thursday and Friday or any other selection.