Mein Rücken knackt manchmal nach dem Sport, deshalb dehne ich mich langsam.

Because Rücken is the subject of the first clause, so it is in the nominative case.

• Rücken is a masculine noun
• the masculine nominative form of mein is mein

So:

• mein Rücken = correct for the subject
• meinen Rücken would be accusative, used for a direct object
• meine Rücken would be plural

Example:

• Mein Rücken knackt.
• Ich dehne meinen Rücken.

Knackt is the 3rd person singular present tense form of knacken.

It matches mein Rücken, which is grammatically he/it in German:

• ich knacke
• du knackst
• er/sie/es knackt

German often uses the present tense for things that happen regularly or sometimes, so knackt manchmal is a natural way to say that this happens from time to time.

In a normal German main clause, the conjugated verb usually comes in second position.

Here the first position is taken by Mein Rücken, so the verb knackt must come next:

• Mein Rücken | knackt | manchmal | nach dem Sport

Manchmal is an adverb, and adverbs often come later in the clause.

You can also move manchmal for emphasis:

• Manchmal knackt mein Rücken nach dem Sport.

That is also correct.

Because nach takes the dative case when it means after.

• Sport is masculine
• the masculine dative article is dem

So:

• nach dem Sport = after sport / after exercise

This same pattern appears in many other expressions:

• nach dem Essen
• nach dem Unterricht
• nach der Arbeit

Because the sentence contains two complete main clauses:

• Mein Rücken knackt manchmal nach dem Sport
• deshalb dehne ich mich langsam

A comma is commonly used to separate them.

Also, deshalb does not create a subordinate clause. It is not like weil. It links the idea of the first clause to the second one, but the second clause still keeps normal main-clause word order.

Because German main clauses follow the verb-second rule.

If deshalb is placed first, then the conjugated verb must come immediately after it:

• deshalb dehne ich mich langsam

Structure:

• deshalb = position 1
• dehne = position 2
• ich = subject after the verb

This is very common in German:

• Heute gehe ich nach Hause.
• Dann rufe ich an.
• Deshalb dehne ich mich langsam.

Because sich dehnen is commonly used as a reflexive verb in German.

So German says:

• ich dehne mich
• du dehnst dich
• er dehnt sich

In English, you can often just say I stretch, but German very often uses the reflexive pronoun here.

There is also a non-reflexive version when you name what you are stretching:

• Ich dehne meinen Rücken.
• Ich dehne meine Beine.

But in your sentence, Ich dehne mich means I stretch myself / I do stretching.

Mich is the accusative reflexive pronoun for ich.

Reflexive pronouns change depending on the subject:

• ich → mich
• du → dich
• er/sie/es → sich
• wir → uns
• ihr → euch
• sie/Sie → sich

So:

• Ich dehne mich
• Du dehnst dich
• Er dehnt sich

Here it is an adverb, because it describes how the stretching happens.

German does not usually add a special ending like English -ly. The same basic form can often be both adjective and adverb.

So:

• ein langsamer Bewegungsablauf = adjective
• ich bewege mich langsam = adverb
• ich dehne mich langsam = adverb

So langsam here means slowly.

Yes, but the structure and focus change.

Deshalb means therefore / for that reason and starts a main clause:

• Mein Rücken knackt manchmal nach dem Sport, deshalb dehne ich mich langsam.

If you use weil, you create a subordinate clause, and the verb goes to the end:

• Ich dehne mich langsam, weil mein Rücken manchmal nach dem Sport knackt.

So both can express a similar idea, but the grammar is different:

• deshalb → main clause, verb in second position
• weil → subordinate clause, verb at the end

Two sounds may be especially tricky for English speakers:

ü in Rücken

• This sound does not exist in standard English
• A useful trick: say ee while rounding your lips

ch in ich

• This is the soft German ich sound
• It is not like English k
• It is not like ch in church

A rough guide:

• Rücken sounds somewhat like RUE-ken, but with a real German ü
• ich ends with the soft ch sound, not ik

If you want, I can also break the whole sentence down word by word for pronunciation.