My si můžeme hrát v parku.

Because the verb form můžeme already tells you the subject is we. Czech often leaves my out unless it is needed for emphasis, contrast, or clarity.

So:

• Můžeme si hrát v parku. = neutral, ordinary We can play in the park.
• My si můžeme hrát v parku. = we can play in the park, possibly contrasting with someone else

In other words, my is not required here, but it adds emphasis.

In this sentence, si does not translate neatly as a separate English word. It is part of the expression hrát si, which means to play in the sense of have fun / play around, especially for children.

So although si is historically a reflexive form, here you should mostly learn hrát si as a unit.

It does not mean ourselves in a direct English-style way.

This is a very common Czech word-order issue.

The dictionary form is hrát si. But si is a clitic, meaning a short unstressed word that usually goes in the second position in the sentence.

That is why you get:

• Můžeme si hrát v parku.
• My si můžeme hrát v parku.

Even though si belongs with hrát, it often moves forward in the sentence because of Czech clitic placement.

So yes, the verb is still hrát si even when si is separated from hrát.

This distinction is important:

• hrát often means to play something

  • hrát fotbal = to play football
  • hrát na piano = to play the piano
  • hrát roli = to play a role

• hrát si usually means to play for fun, especially like children do

  • Děti si hrají. = The children are playing.

So in a sentence about being in a park and playing around, hrát si is the natural choice.

Usually not if you mean play around / have fun.

Without si, hrát often sounds like it needs an object or a more specific activity:

• Můžeme hrát fotbal v parku. = We can play football in the park.
• Můžeme hrát divadlo v parku. = We can perform theater in the park.

So if you mean general play, especially children playing, keep si:

• Můžeme si hrát v parku.

Můžeme is the 1st person plural present tense form of moci, which means can / to be able to.

So:

• mohu / můžu = I can
• můžeš = you can
• může = he/she/it can
• můžeme = we can
• můžete = you can
• mohou / můžou = they can

Here, můžeme matches my = we.

It can mean either, depending on context.

So the sentence may express:

• ability: we are able to play in the park
• permission: we are allowed to play in the park

In everyday Czech, můžeme often covers both ideas. If you want to make permission especially clear, Czech can also use smět:

• Smíme si hrát v parku. = We may / are allowed to play in the park.

But můžeme si hrát v parku is completely normal.

Because the preposition v meaning in or inside/at takes the locative case when it describes location.

The noun park changes in the locative singular:

• park = park
• v parku = in the park

So the form parku is required by the preposition v in this meaning.

It is locative singular.

Why?

• v
  • location usually requires the locative
• park is a masculine inanimate noun
• its locative singular form is parku

So:

• park = nominative
• v parku = locative after v

Yes, very often.

Czech v plus the locative can cover meanings that English sometimes expresses as either in or at, depending on context.

So v parku is usually the normal way to say that the activity happens in that park area. In many situations, translating it as either in the park or at the park would be fine.

It can change, but not completely freely.

A neutral version would usually be:

• Můžeme si hrát v parku.

Your sentence:

• My si můžeme hrát v parku.

sounds more emphatic because my is stated explicitly.

You can also move parts around for emphasis:

• V parku si můžeme hrát. = It is in the park that we can play.
• Hrát si můžeme v parku. = Playing is something we can do in the park.

However, si still follows the usual clitic-placement rules, so some word orders are much more natural than others.

Yes, but it is not the most neutral version.

The most neutral everyday sentence is:

• Můžeme si hrát v parku.

Adding my makes it sound more contrastive or emphatic, for example:

• Oni ne, ale my si můžeme hrát v parku.
  They can’t, but we can play in the park.

So the sentence is correct and natural in the right context, especially when we is being emphasized.