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@Harten

What is the meaning of this sentence?

This is often the wrong question — even when the sentence is perfectly grammatical, conventionally punctuated, and written by a native speaker.

what exactly is the speaker trying to say?

This, as always, is the right question. But the answer can't be found in that sentence alone.
We need to use every clue we can find in the context and in the rest of the text.

You say it's the caption to a posting. A working hypothesises, then, is that it adds no information to the body of the text, but is simply intended to catch the eye,

what is the tone of the speaker? Is it inciting?

These questions can't possibly be answered on the basis of that one sentence.

The exclamation mark gives a vague hint at the tone. It's emphatic in some way.
But there is no proposition in the sentence, so we can't tell what the writer is trying to emphasise.

The only course of action expressed in the sentence is they be taught a lesson.
However this PASSIVE expression doesn't include an AGENT. So there is nobody to incite to 'teach them a lesson'.

Either your questions are unanswerable or the answers lie in the body of the post.
I can make some guesses.

Should they be taught!
The exclamation mark suggests that the — a speaker of the language of country X — does not mean it as a question.
It's possible that he/she is

• mistranslating a SUBJUNCTIVE in the language of X
• bringing the MODAL VERB should to the front of the clause — on the mistaken analogy with may,
  as in May the King live for ever!
  or May you live interesting times!

in their own ways
This grammatical but meaningless.

You are certain that they refers to the citizen body of country Y.
So it might make sense to use SINGULAR in their own way.
The PLURAL suggests that each citizen of has his or her own way.

a lesson in
The problem here is that in is grammatically ambiguous.
It's quite likely that the writer intend it as part of the phrase in their own ways.
But there's another interpretation — which is a reader more likely to make at first glance.
Usually, a lesson in Z = 'a lesson on how to do Z'

1-Now does asking with "When" make sense? And in what case could it make sense?

Yes, it does makes sense — because we understand when to mean 'before' when there's a PAST PERFCT form in the MAIN CLAUSE. It's clearer and sound better to use the word Before, but it's not ungrammatical to use When.

2-Also someone (Probably American) would say "Before you worked in your last job, did you have your own office" is this grammatically correct?

I think speakers of other dialects — including British English — would find it perfectly acceptable.

There's a slight difference in how a hearer/reader might understand the two sentences

• Before you worked in your last job, did you have your own office?
  This might be understood to refer one job before the last one.

• Before you worked in your last job, had you had your own office?
  This might be understood to refer all the jobs before the last one.
  (This meaning can be made explicit by using the word ever.)

The poet leaves it for the reader to interpret. Here's how I read it. Others may read it quite differently.

Sky's crying,
me

I take this to mean that somebody else says the sky is crying, and that the poet will say what he or she thinks.

either...

The poet has deliberately omitted the words that would make this grammatical and informative.
My reading is that either is not introducing two alternatives that will be expressed.
Rather (as I read it) it's tagged on to two expressions that have already been made.
Either is used to follow two negative statements. So what could they be?

• I take me either to imply 'I don't either'.
• The preceding negative statement would have to be 'X doesn't'.
  So who is X and what don't they do? This depends on how you read the next lines.

call that rain

Rightly or wrongly, I read this as a challenging denial.
Alternatively, it could mean 'Call this weather condition rain and don't call it anything else'.

Call me pain

The capital letter suggests to me that this line — unlike the precious two — marks a break, a new idea.
Rightly or wrongly, I read this as 'Never mind all that sky and rain business. It's me that's in pain'.

On the basis of these reading, I take the unexpressed idea between lines 1 and 2 to be 'You, reader, don't think that the sky is crying'

North Magnetic Pole is what the pole is called. Keep in mind that the word 'North' can be used as a noun ("My parents have moved to the north"); an adverb ("The birds fly north every year"); or as an adjective ("The north side of town is better"). Usually, the adjectives northern, southern etc refer to a bigger area (e.g. the Northern Hemisphere; Eastern Europe). In the case of the magnetic pole, it is a point on Earth, therefore small in comparison.
You're right to consider "northern" a modifier. It is an adjective.

Hope this helps.

No, @Ahmed_Ashraf, eating can only be used in an ACTIVE sense here.

The construction is a shortened version of

...the special foods that are eaten

So you can say

Who are the special people eating at the festival?

because it's a shorten version of

...the people who are eating

SORRY!

It's a tricky argument, and I got it wrong in my last posting.

I think the discussion still stands for DIFFERENT SUBJECTS in the two clauses.
But I need to rewrite the discussion of DIFFERENT VERBS. The first part is OK, I think.

B.
If the second clause differs only in the VERB, then the scope of too is the rest of the PREDICATE after the VERB.
A technical term for this is COMPLEMENTATION.

If the SCOPE of too is the COMPLEMENTATION, not the SUBJECT, then it doesn't matter whether the SUBJECTS in the two clauses are the same or different.

• Peter (or John) gave Jo an apple willingly on Thursday. Peter (or John) sold Jo an apple willingly on Thursday.
  Because the COMPLEMENTATIONS are the same,
  — We can add too
  — We can link them with and, not but

• Peter (or John) gave Jo an apple willingly on Thursday, and he sold Jo an apple willingly on Thursday too.

But the rest of the argument is wrong. My mistake was

Add NEGATION to the PREDICATES in both clauses. The SCOPE of NEGATION is the COMPLEMENTATION in each clause.

But this isn't so. The VERB is NEGATIVE but the COMPLEMENTATION is the same in both clauses:
Jo an apple willingly on Thursday

So the next part of the argument is OK, I think

• Peter (or John) didn't give Jo an apple willingly on Thursday. Peter (or John) didn't sell Jo an apple willingly on Thursday.
  Because the COMPLEMENTATIONS are the same,
  — We can add too (although either sounds better)
  — We can link them with and, not but
  Peter didn't give Jo an apple willingly on Thursday, and he didn't sell him one willingly on Thursday too (or either).

But the next part of my argument was wrong:

But if only one of the PREDICATES is negative, then the COMPLEMENTATIONS are different

In fact the COMPLEMENTATION is

Jo an apple willingly on Thursday

This is the same even when only one of the PREDICATES is negative

However, it makes a difference which of the two clauses is negative

• Peter (or John) gave Jo an apple willingly on Thursday. Peter (or John) didn't sell Jo an apple willingly on Thursday.

  Because the COMPLEMENTATIONS are the same and the first clause is positive
  — We can add too
  Because the PREDICATES are different,
  — We can link them with but, not and
  Peter (or John) gave Jo an apple willingly on Thursday, but he didn't sell Jo an apple willingly on Thursday too.

• Peter (or John) didn't give Jo an apple willingly on Thursday. Peter (or John) sold Jo an apple willingly on Thursday.
  Because the COMPLEMENTATIONS are the same but the first clause is negative
  — We can't add too
  Because the PREDICATES are different,
  — We can link them with but, not and
  Peter (or John) didn't give Jo an apple willingly on Thursday, but he sold Jo an apple willingly on Thursday.

@Prudence, the vocabulary of the senses can be tricky.

Let's start with sound and sight. English has verbs for

1. a person making an effort
2. a person having an experience, without making an effort
3. a thing affecting a person

So for sound

1. I listened.
2. I heard a dog.
3. The dog sounded angry.

For sight

1. I looked.
2. I saw the flower.
3. The flower looked pretty

For sight the verb look is used for [1] and [3]. For taste there is even less variety.

1. I tasted.
2. I tasted the soup.
3. The soup tasted salty.

Now there is another verb. It's a two-word verb taste of. We use it

• only for [3]
• referring not to the object tasted but to the strongest ingredient

So we can say

1. I tasted.
2. I tasted the soup.
   3a. The soup tasted good.
   3b. It tasted of asparagus.

Now your question only makes sense with meaning [2]. If you say

May I taste of it?

It means

'Please cover me with it, so that when somebody eats me they will taste it — more strongly than they'll taste my flesh.'

which is not what you mean.

There is a four-word verb you could use: have a taste of. So you could say

May I have a taste of it?