Po zajęciach gramy w grę.

Because the preposition po usually requires the locative case when it means after in a time expression.

• dictionary form: zajęcia
• locative plural: zajęciach

So:

• po zajęciach = after classes / after the lesson(s)

This is a fixed and very common pattern in Polish:

• po pracy = after work
• po szkole = after school
• po zajęciach = after classes

The basic form is zajęcia.

In school or course contexts, zajęcia often means classes, lessons, or sessions. Polish very often uses the plural here even when English might say after class in the singular.

So:

• zajęcia = classes / lessons / class sessions
• po zajęciach = after class / after classes

There is also a singular noun zajęcie, but in the education sense Polish commonly uses the plural form zajęcia.

Gramy is the 1st person plural form of grać.

It means:

• we play
• or we are playing, depending on context

Polish present tense often covers both the simple present and the present continuous meanings that English separates.

So gramy by itself already tells you the subject is we.

Because Polish usually does not need a subject pronoun when the verb ending already shows who is doing the action.

Here, -my in gramy already means we.

So:

• gramy = we play
• my gramy = we play, but with extra emphasis or contrast

You would add my only if you want to stress it, for example:

• My gramy, a oni pracują. = We are playing, and they are working.

Because with many games, Polish uses the pattern grać w + accusative.

So:

• grać w szachy = to play chess
• grać w karty = to play cards
• grać w tenisa = to play tennis
• grać w grę = to play a game

This is just the normal structure used with grać for participating in a game.

Be careful: grać can also appear in other patterns:

• grać na gitarze = to play the guitar
• grać rolę = to play a role

So the preposition depends on what kind of playing you mean.

Because after w in this pattern, the noun goes into the accusative case.

The noun is:

• nominative: gra
• accusative: grę

So:

• w grę

This is a regular change for many feminine nouns ending in -a:

• książka → książkę
• kawa → kawę
• gra → grę

Yes, it is grammatical and natural, but it is a bit generic.

It simply means we play a game. In real conversation, Polish often names the specific game instead:

• Gramy w szachy.
• Gramy w karty.
• Gramy w Monopoly.

So gramy w grę is fine when you mean a game in a general sense, but very often speakers would specify which game.

Yes. Polish word order is more flexible than English because case endings show the grammatical roles.

Po zajęciach gramy w grę is a neutral, natural order.

You could also say:

• Gramy w grę po zajęciach.

That means the same thing, but the focus shifts slightly. The original sentence puts after classes first, which makes the time setting feel more prominent.

So the order can change, but different orders can sound more or less natural depending on what you want to emphasize.