Posle bazena obično jedem sendvič i pijem vodu.

Because the preposition posle (after) requires the genitive case.

• Basic noun: bazen = pool
• After posle, it becomes bazena

So:

• bazen = the pool
• posle bazena = after the pool / after going to the pool

This is a very common pattern in Serbian: certain prepositions always force a specific case.

Because vodu is the accusative singular form of voda, and here it is the direct object of pijem (I drink).

• Nominative: voda = water
• Accusative: vodu = water, as the thing being drunk

So:

• Voda je hladna. = The water is cold.
• Pijem vodu. = I am drinking water / I drink water.

For many feminine nouns ending in -a, the accusative singular changes to -u.

Because sendvič is a masculine inanimate noun, and in Serbian, the accusative singular of masculine inanimate nouns is usually the same as the nominative singular.

So:

• Nominative: sendvič
• Accusative: sendvič

That is why you say:

• Jedem sendvič. = I eat / I am eating a sandwich.

Compare that with a feminine noun like voda, which changes form in the accusative.

In Serbian, subject pronouns are often omitted because the verb ending already shows who the subject is.

• jedem = I eat
• pijem = I drink

So ja is not necessary.

You can say:

• Posle bazena obično jedem sendvič i pijem vodu.

And it already clearly means I usually eat a sandwich and drink water after the pool.

If you add ja, it sounds more emphatic:

• Ja obično jedem sendvič... = I usually eat a sandwich...

Obično means usually. It shows that this is a habitual action, not just something happening once.

So the sentence means something like:

• After the pool, I usually eat a sandwich and drink water.

Without obično, the sentence would simply say:

• Posle bazena jedem sendvič i pijem vodu.
  = After the pool, I eat / am eating a sandwich and drink / am drinking water.

With obično, the meaning becomes more clearly routine or repeated.

Because Serbian, like English, often uses the present tense for habits and routines.

Here:

• jedem = I eat / I am eating
• pijem = I drink / I am drinking

Since obično means usually, the present tense is understood as a repeated habit:

• I usually eat
• I usually drink

So this is not about one specific future or past event. It is about what the speaker generally does.

Yes. Serbian word order is fairly flexible, and obično can often move around, although some placements sound more natural than others.

For example:

• Posle bazena obično jedem sendvič i pijem vodu.
• Obično posle bazena jedem sendvič i pijem vodu.

Both are natural. The difference is mostly one of emphasis:

• Posle bazena obično... emphasizes after the pool
• Obično posle bazena... emphasizes the idea of usually

Serbian often uses word order to highlight what is most important in context.

Here it expresses time, not location.

Posle bazena means something like:

• after going to the pool
• after swimming
• after being at the swimming pool

Even though the literal words are after the pool, the natural meaning is temporal: what happens once that activity or visit is over.

So it does not mean you are physically standing behind a pool.

Yes. Nakon also means after and also takes the genitive case, so:

• nakon bazena = after the pool

Both are correct, but there can be a slight style difference:

• posle is very common and everyday
• nakon can sound a bit more formal or neutral, depending on context

In ordinary conversation, posle bazena is extremely natural.

Because in Serbian, a short adverbial phrase at the beginning of a sentence usually does not need a comma.

So this is normal:

• Posle bazena obično jedem sendvič i pijem vodu.

You might see commas used sometimes for emphasis or rhythm, but in a plain neutral sentence, no comma is the standard choice.

Jesti (to eat) and piti (to drink) are imperfective verbs in this sentence, and that makes sense because the sentence describes a habit.

In Serbian, imperfective verbs are commonly used for:

• repeated actions
• ongoing actions
• general habits

Since the speaker is talking about what they usually do after the pool, imperfective verbs are the natural choice:

• jedem = I eat / I usually eat
• pijem = I drink / I usually drink

Perfective verbs would not fit as naturally here for a general routine.

Usually a sandwich.

Serbian does not have articles like a and the, so sendvič by itself can mean:

• a sandwich
• the sandwich

The exact meaning depends on context.

In this sentence, because it describes a routine and gives no specific previous reference, English naturally translates it as a sandwich:

• I usually eat a sandwich and drink water.

If the context had already introduced a specific sandwich, English might use the sandwich, but Serbian would still just say sendvič.