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Based on the well-documented experiences of contemporary peers as well as those of past figures in the political arena, many of whom saw their professional reputations and their personal lives deeply and negatively affected as a consequence of releasing their own memoirs upon completing their tenures in leading public positions, the newly retired four-star general, whom, at his farewell press conference, the president himself had taken the time to praise as his most valuable asset in his administration, decided against writing his own book detailing his life, choosing instead to remove himself from the public eye to spend his golden years at his lakeside cottage with his wife of over 40 years, Dolores.

Is this a simple, compound or complex sentence?

I can see only one complete sentence with phrases and some non-restrictive clauses.

Thanks in advance

@Leess

A. What do you mean by the font variation? (ing vs ing)

B. It's difficult to discuss the concept grammatical function. I'm not sure what it would mean in traditional grammar. I'll try to answer you in terms of what some modern grammars mean by grammatical function.

First of all, -ing is not a function but a form. It's a word fragment (technically known as a morpheme) which combines with the bare form of a verb. In this case, the combination forms are selling and travelling.

Now these -ing forms of verbs, these words do have grammatical functions.

ONE
Some -ing words can function like ADJECTIVES. One example is travelling, as in
a travelling salesman
The other word can do the same — but only as part of a compound, as in
_ a best-selling author_

Strictly speaking, these are not adjectives. We can't say
a more travelling salesman or a very best-selling author.
And although we can say
This salesman is travelling
it means something different from
This is a travelling salesman
And we don't say
This author is best-selling
but rather
This author is a best-seller

But some -ing words have become adjectives, for example
very interesting, more annoying, the most exciting
The book is interesting, The boy is annoying, the race is exciting

There is a term for the function of all these words, whether adjectives or not. The term is PREMODIFIER.

And it's important to note that premodifiers function within a NOUN PHRASE.

TWO
Just as an -ing word-fragment combines with a verb to make a one-word form, so in turn an
-ing word may combine with a form of be to make a meaningful unit.
Here's a list for sell:
am/is/ are selling
was/were selling
have/has/had been selling
can/could/will/would/must/might etc be selling

The are termed FINITE VERB FORMS. Specifically they are the PROGRESSIVE finite verb forms.
Their grammatical function is within a CLAUSE.

The grammatical function of a finite verb form is to hold the clause together.
In order for a clause to be grammatical

• all finite forms demand a SUBJECT
• the structure of the rest of the clause is determined by the verb from which the finite form is made. For example:
  — sell normally demands an OBJECT (such as insurance)
  — travel normally does not demand an OBJECT, but may be followed by an ADVERBIAL (such as to Finland)
  — put demands both an OBJECT and an ADVERBIAL (e.g. She put the book on the table_)
  — give_ demands a DIRECT OBJECT and either an INDIRECT OBJECT or an ADVERBIAL
  (e.g. He gave her the flowers or He gave the flowers to her.)

It's common to use the word verb to refer to a function or a form or a word class.
So some modern grammars use the term PREDICATOR for the grammatical function.

THREE
FINITE CLAUSES in turn have a grammatical function within a SENTENCE. This may be:

• the only clause — e.g. She is selling insurance.
• the MAIN CLAUSE — e.g. She is selling insurance because she needs the work.
• a SUBORDINATE CLAUSE — e.g. She wears a business suit when she's selling insurance.

FOUR
This where we come to selling and travelling in your examples. I'll discuss this in a new post.

FOUR
This where we come to selling and travelling in your examples.

Each is part of what used to be called a phrase.
selling insurance and travelling to Finland

Modern grammars call these NON-FINITE CLAUSES because they are grammatically almost the same as FINITE CLAUSES.

• The main difference is that the are often without a SUBJECT — as in your two examples
• However the structure of the clause is controlled by the verb is the same way, whether the verb form is finite or non-finite.

There are two other types of NON-FINITE CLAUSE built around different NON-FINITE forms.

• TO-INFINITIVE — e.g. She moved to the Northeast to sell insurance.
• BARE INFINITIVE — e.g. We watched her travel to Finland.

FIVE
NON-FINITE CLAUSES can have different grammatical functions within SENTENCES.
Some are the same functions that can be fulfilled by NOUN PHRASES.

• SUBJECT — Selling insurance is profitable. Travelling to Finland will be enjoyable.
• OBJECT — I regret selling insurance. I recommend travelling to Finland.
• after a PREPOSITION —It was a scheme for selling insurance. It's an article about travelling to Finland.

Another common grammatical function within a sentence is as ADVERBIAL.
You can see this by substituting a one-word ADVERB with the same grammatical function.
She works the Northeast region of the state enthusiastically.
Gradually I found the weather got colder and colder.

I know that it is correct to say "a review of a new musical". Is it also correct to say "a review for a new musical"?

The point is that I came across "There are mostly five-star reviews for the product on Amazon" in
https://housebeautiful.com/shopping/a26026219/shower-curtain-liner-holds-phone-ipad/

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.