Na het sporten rek ik mijn arm en mijn nek, zodat ze niet stijf worden.

Here sporten is being used as a noun-like infinitive: literally, the exercising.

So:

• sporten = to exercise / to play sports
• het sporten = exercising

After na you often get a noun phrase, so na het sporten means after exercising.

This is a very common Dutch pattern:

• na het eten = after eating
• tijdens het lezen = while reading
• voor het slapen = before sleeping

Yes, you may hear na sporten in everyday Dutch, and it is understandable. But na het sporten is more complete and standard in careful written Dutch.

So:

• na het sporten = very standard
• na sporten = common, a bit shorter/more colloquial

Both can mean after exercising.

This is because Dutch main clauses follow the verb-second rule.

The sentence starts with Na het sporten, which takes the first position. The finite verb must then come second, so you get:

• Na het sporten rek ik ...

If you started with the subject, you would say:

• Ik rek mijn arm en mijn nek na het sporten.

Both are grammatical. The version in your sentence puts the time phrase first for emphasis or natural flow.

Yes. Rekken is a normal word for stretching your body or a body part.

So:

• ik rek mijn arm = I stretch my arm
• ik rek mijn nek = I stretch my neck

A related verb is strekken, but that often means to extend, straighten, or stretch out in a more formal or physical-position sense. For everyday exercise and warm-up/cool-down language, rekken is very natural.

Because mijn arm en mijn nek refers to two things together:

• one arm
• one neck

Even though each noun is singular, the combination joined by en is plural in meaning. That is why Dutch uses:

• ze = they
• worden = become / get, plural form

Compare:

• mijn arm ... zodat hij niet stijf wordt = my arm ... so that it doesn’t get stiff
• mijn arm en mijn nek ... zodat ze niet stijf worden = my arm and my neck ... so that they don’t get stiff

Both can mean they, but ze is the normal unstressed form.

In this sentence, there is no special emphasis, so ze is the natural choice:

• zodat ze niet stijf worden

You would use zij if you wanted emphasis or contrast:

• ... zodat zíj niet stijf worden
• Niet mijn benen, maar zij

So here, ze is simply the ordinary choice.

Zodat means so that.

It introduces a subordinate clause, and in Dutch subordinate clauses, the verb usually goes to the end. That is why you get:

• zodat ze niet stijf worden

Breakdown:

• zodat = so that
• ze = they
• niet stijf = not stiff
• worden = become / get

The comma before zodat is also normal, because Dutch usually separates this kind of subordinate clause with a comma.

Because worden focuses on becoming stiff, not simply being stiff.

• stijf zijn = to be stiff
• stijf worden = to become / get stiff

In this sentence, the idea is preventive: after exercising, I stretch them so that they do not get stiff.

If you said zodat ze niet stijf zijn, that would sound more like so that they are not stiff, which is less natural here because the concern is about what happens afterward.

Yes, mijn arm en nek is possible and understandable.

Dutch often allows either:

• mijn arm en mijn nek
• mijn arm en nek

Repeating mijn can make the sentence a bit clearer or more balanced, especially in careful speech or writing. Without the second mijn, the meaning is still clear: both the arm and the neck are yours.

So the repeated possessive is natural, but not absolutely required.

Yes. Dutch very often uses possessives with body parts:

• ik was mijn handen = I wash my hands
• mijn rug doet pijn = my back hurts
• ik rek mijn nek = I stretch my neck

So mijn arm and mijn nek are completely normal Dutch.

Yes, arm is singular on purpose: the sentence literally says my arm and my neck.

If you want to say my arms and my neck, you would say:

• Na het sporten rek ik mijn armen en mijn nek, zodat ze niet stijf worden.

So:

• arm = arm
• armen = arms

The rest of the sentence can stay the same.