Jeg tar meg av barna i kveld.

Because å ta seg av is a fixed expression in Norwegian. It means to take care of, to look after, or sometimes to deal with someone or something.

So in this sentence, you should understand:

• ta = take
• ta seg av = take care of / look after as a whole expression

You usually cannot translate it word-for-word and get natural English. It works like a set phrase.

Meg is the reflexive part of the expression å ta seg av.

With jeg, the reflexive pronoun is meg:

• jeg tar meg av = I take care of
• du tar deg av = you take care of
• han/hun tar seg av = he/she takes care of
• vi tar oss av = we take care of

So meg is not being used in the ordinary sense of me here. It is part of the verb pattern.

No — not in this expression.

In å ta seg av, av is a required part of the phrase. It is similar to how English phrasal verbs need their particle:

• look after
• take care of

If you remove av, the meaning changes or the sentence becomes wrong for this meaning.

So:

• Jeg tar meg av barna = correct
• Jeg tar meg barna = wrong for this meaning

Barna is the definite plural form of barn.

Here is the pattern:

• et barn = a child
• barnet = the child
• barn = children
• barna = the children

So barna means the children, not just children.

Because Norwegian usually puts definiteness at the end of the noun.

English uses a separate word:

• the children

Norwegian often uses a suffix:

• barna

So barna already includes the idea of the.

You would not normally say de barna here unless you specifically mean something like those children or you are being extra specific in context.

Norwegian often uses the present tense for near-future actions when the time is clear from the sentence.

So:

• Jeg tar meg av barna i kveld
  literally uses present tense, but it can mean I’m taking care of the children tonight or I’ll take care of the children tonight.

The time expression i kveld makes it clear that this is about tonight, so Norwegian does not need a special future form.

I kveld means this evening or tonight, depending on context.

In this sentence, it tells you when the action happens.

• i = in
• kveld = evening

But you should learn i kveld as a time expression meaning tonight / this evening.

Yes. Time expressions are often flexible in Norwegian.

You can say:

• Jeg tar meg av barna i kveld.
• I kveld tar jeg meg av barna.

Both are natural.

If you move i kveld to the front, Norwegian still follows the verb-second rule, so tar must come before jeg:

• I kveld tar jeg ...
• not I kveld jeg tar ...

Mostly yes, for this expression.

The usual order is:

• tar + reflexive pronoun + av + object

So:

• Jeg tar meg av barna
• Hun tar seg av hunden
• Vi tar oss av problemet

You should think of ta seg av as a unit, and then add the thing or person being looked after after av.

Sometimes, yes, but the meaning may be slightly different.

For example:

• Jeg passer barna i kveld = I’m babysitting / watching the children tonight
• Jeg tar meg av barna i kveld = I’m taking care of the children tonight

Ta seg av is a bit broader. It can mean general responsibility, care, or looking after someone. Passe is often more specifically watch, mind, or babysit.

So the sentence you have is natural and idiomatic, especially if the idea is general care or responsibility.