Můj kamarád chce jít do tělocvičny, protože si tam můžeme hrát s míčem.

Because kamarád is a masculine singular noun in the nominative case, and můj has to agree with it.

• můj kamarád = my male friend
• moje kamarádka = my female friend
• moje auto = my car

So the form of my changes depending on the gender and case of the noun.

Yes. Kamarád is grammatically masculine and normally refers to a male friend. If you mean a female friend, you would usually say kamarádka.

This is a very common Czech pattern:

• kamarád = male friend
• kamarádka = female friend

Because Czech, like English, often uses want + infinitive.

• chce = wants
• jít = to go

So chce jít literally works like wants to go.

Here, chce is the 3rd person singular present form of chtít.

These verbs all relate to going, but they are used differently.

• jít = to go on a specific occasion, usually on foot
• chodit = to go regularly / habitually
• jet = to go by vehicle

So here jít fits because the sentence is about one intended trip.

Compare:

• Chce jít do tělocvičny. = He wants to go to the gym.
• Chodí do tělocvičny. = He goes to the gym regularly.
• Chce jet do tělocvičny. = He wants to go to the gym by vehicle.

The preposition do takes the genitive case when it means movement into or to a place.

The base form is:

• tělocvična = gym / gymnasium / sports hall

After do, it becomes:

• do tělocvičny

So tělocvičny is genitive singular.

A useful contrast:

• do tělocvičny = to the gym
• v tělocvičně = in the gym

Not always. Tělocvična usually means a gymnasium / sports hall, especially a place for PE classes or ball games.

If you mean a fitness gym with weights and machines, Czech often uses:

• posilovna = weight room / fitness gym

So in this sentence, tělocvična makes sense because it mentions playing with a ball.

Because protože introduces a subordinate clause, and in Czech those are normally separated by commas.

So:

• Můj kamarád chce jít do tělocvičny, protože...

This is standard Czech punctuation.

Protože means because and introduces the reason.

So the sentence has:

• a main clause: Můj kamarád chce jít do tělocvičny
• a subordinate clause giving the reason: protože si tam můžeme hrát s míčem

Unlike some languages, Czech does not force the verb to go to the very end of the subordinate clause.

Because hrát si is a very common expression meaning to play / to have fun / to play around.

That is different from plain hrát, which often means things like:

• to play a game or sport
• to play an instrument
• to act a role

So:

• hrát si s míčem = to play with a ball
• hrát fotbal = to play football
• hrát na kytaru = to play guitar

Here, si is not really translated as a separate English word. It is just part of the natural Czech expression hrát si.

Because Czech usually leaves out subject pronouns when the verb ending already shows who the subject is.

• můžeme = we can

The ending -me already tells you it means we, so my is unnecessary unless you want extra emphasis or contrast.

For example:

• Můžeme si tam hrát. = We can play there.
• My můžeme si tam hrát, ale oni ne. = We can play there, but they can't.

The preposition s meaning with takes the instrumental case.

The noun is:

• míč = ball

In the instrumental singular, it becomes:

• míčem

So:

• s míčem = with a ball

This is a very common pattern:

• s kamarádem = with a friend
• s autem = with a car
• s míčem = with a ball

Czech word order is fairly flexible, but short unstressed words like si tend to go very early in the clause.

After protože, the natural order is:

• protože si tam můžeme hrát s míčem

That is why si appears so early.

In a main clause, you could also say things like:

• Tam si můžeme hrát s míčem.
• Můžeme si tam hrát s míčem.

But directly after protože, si near the beginning is the normal pattern.

Tam means there. It points back to the gym and emphasizes that that is the place where the playing can happen.

So the idea is:

• in that place / there, we can play with a ball

Czech often uses words like tam even where English might leave them out or make them sound lighter. It helps connect the second clause clearly to the location just mentioned.