Learn Hardcore Norwegian: Denne uken er hektisk, derfor tar jeg fri i helgen. - This week is hectic, therefore I take time off on the weekend.

Norwegian normally uses the definite form with demonstratives: denne + [definite noun].
So you get denne uken (this week), denne boken (this book), etc.
Using denne uke is not standard in Bokmål (and would sound “off” to most speakers).

What’s the difference between uken and uka here?

Both mean the week, but:

uken is the more formal/common Bokmål form.
uka is also Bokmål (often more colloquial) and very common in speech.

So you may also hear: Denne uka er hektisk, derfor tar jeg fri i helgen.

Why is there a comma before derfor?

Because the sentence has two main clauses: 1) Denne uken er hektisk
2) derfor tar jeg fri i helgen

It’s very common in Norwegian to separate two independent clauses with a comma, especially when the second starts with a linking adverb like derfor, likevel, dessuten, etc.
In more formal writing, a semicolon can also work: Denne uken er hektisk; derfor tar jeg fri i helgen.

Why is the word order derfor tar jeg and not derfor jeg tar?

Norwegian main clauses follow the V2 rule: the finite verb must be in the second position.
When derfor is put first, the verb still has to be second, so the subject moves after the verb:

Derfor tar jeg fri ... (Therefore, I take time off …)

If you kept subject + verb after derfor (derfor jeg tar), it would sound like a non-standard structure (or like something incomplete) in normal Bokmål main-clause grammar.

Is derfor a conjunction like so, or something else?

Derfor is an adverb meaning therefore / for that reason. It links ideas, but grammatically it behaves like an adverb, which is why it triggers V2 word order when placed first in a main clause.

If you want something closer to the English conjunction so, you can also use så in some contexts, but it doesn’t always match the same style/meaning as derfor.

What does tar jeg fri literally mean, and is it an idiom?

Yes, it’s a common expression. Literally it’s I take free, but idiomatically it means:

to take time off
to take a day off / have time off

You can vary it:

Jeg tar fri på fredag. (I’m taking Friday off.)
Jeg tar en fridag. (I’m taking a day off.)

Could I also say jeg har fri instead of jeg tar fri?

Yes, but it changes the nuance:

jeg tar fri = I choose/plan to take time off (an action/decision)
jeg har fri = I am off / I have time off (a state/schedule)

So in your sentence, derfor tar jeg fri i helgen emphasizes the decision based on the hectic week.

Why is it i helgen and not på helgen?

In Bokmål, the most standard choice for in/at the weekend is i helgen.
You may hear på helga/på helgen in some dialects and informal speech, but i helgen is the safe, widely accepted option (especially in writing).

Why is hektisk not inflected (like hektisk vs hektiske)?

Because it’s a predicate adjective describing a singular noun (uken) after the verb er:

Uken er hektisk. (singular → hektisk)

You’d use plural if the subject were plural:

Disse ukene er hektiske. (plural → hektiske)

Could I switch the order and say Derfor tar jeg fri i helgen, denne uken er hektisk?

You can front the reason clause, but you’d normally rewrite it more naturally, for example:

Siden denne uken er hektisk, tar jeg fri i helgen. (siden = since)
Fordi denne uken er hektisk, tar jeg fri i helgen. (fordi = because)

If you start with derfor, it usually points back to a reason already stated, so it sounds most natural after the first clause (as in your original sentence).