Po deszczu dzieci omijają każdą kałużę, ale pies i tak biegnie przez środek chodnika.

Here deszczu is in the locative singular, because po can mean after, and in that time-related meaning it takes the locative.

So:

• deszcz = rain
• po deszczu = after the rain / after rain

A small tricky point: for some masculine nouns, the locative and genitive singular look the same. That is true here: deszczu could also be genitive in other contexts, but in this sentence it is locative because of po.

Because dzieci means children, so it is a plural subject.

That means the verb must also be plural:

• dziecko omija = the child avoids / goes around
• dzieci omijają = the children avoid / go around

Omijają is the 3rd person plural present form of omijać.

Because omijać takes a direct object, and that object goes into the accusative case.

The basic dictionary forms are:

• każda = every
• kałuża = puddle

In the accusative singular feminine, they become:

• każdą
• kałużę

So:

• każda kałuża = every puddle
• omijają każdą kałużę = they avoid / go around every puddle

This is normal adjective-noun agreement: the adjective and noun both change to match case, gender, and number.

Because każdy / każda / każde means each / every, and it normally goes with a singular noun, just like English every puddle.

Compare:

• każdą kałużę = every puddle
• wszystkie kałuże = all puddles

So the Polish structure matches English quite closely here.

Omijać usually means to go around, to обходить / bypass, or to avoid by not going through something.

In this sentence, it is very physical and concrete: the children are not stepping into the puddles; they are going around them.

That is why omijać works very well here. It is a bit more specific than a general verb like unikać (to avoid), which can also be used in more abstract situations.

So:

• omijać kałuże = to go around puddles
• unikać problemów = to avoid problems

I tak is a very common fixed phrase meaning:

• anyway
• still
• all the same
• regardless

So pies i tak biegnie means something like:

• the dog runs anyway
• the dog still runs
• the dog runs right through despite that

A very important point: here i does not mean a simple and connecting pies with another noun. The subject is just pies. The phrase i tak functions together as one expression.

This is a very natural question, because both relate to running.

• biec / biegnie = to be running, to run in one specific movement/direction
• biegać / biega = to run around habitually, repeatedly, or in general

Here the sentence describes one concrete scene: the dog is running through the middle of the sidewalk. That is why biegnie is the better choice.

Compare:

• Pies biegnie przez ulicę. = The dog is running across the street.
• Pies biega po parku codziennie. = The dog runs around the park every day.

It can mean either, depending on context.

Polish does not have a separate verb form that works exactly like the English present continuous. The present tense often covers both:

• runs
• is running

So pies biegnie could be translated as:

• the dog runs
• the dog is running

In this particular sentence, English often sounds most natural with is still running or runs anyway, depending on how you want to phrase the contrast.

This phrase has two important grammar points.

1. Przez takes the accusative
2. Środek is followed by the genitive of the thing whose middle it is

So:

• przez
  • accusative → środek
• środek czego? = the middle of what? → chodnika

That gives:

• przez środek chodnika = through the middle of the sidewalk

Also, środek is a masculine inanimate noun, and in the singular its accusative form looks the same as the nominative, so it stays środek.

Because środek means middle, and in Polish you usually say the middle of something with the second noun in the genitive.

So:

• środek pokoju = the middle of the room
• środek miasta = the middle of the city
• środek chodnika = the middle of the sidewalk

That is why chodnik changes to chodnika.

Ale means but, and it introduces a clear contrast.

The sentence sets up one behavior:

• the children avoid every puddle

and then contrasts it with another:

• the dog still runs right through the middle

So ale is very natural because it highlights the difference strongly.

In some contexts Polish can use a for contrast too, but ale is stronger and closer to English but.

Because Polish has no articles.

So nouns like:

• deszcz
• dzieci
• pies
• chodnik

do not need words equivalent to the or a/an.

Whether English uses a dog or the dog, a sidewalk or the sidewalk, depends on context and translation style. Polish leaves that unstated unless something else makes it clear.

Yes, but in a natural way.

Po deszczu comes first to set the scene: after the rain. Then we get what the children do, and then the contrast with the dog.

Polish word order is more flexible than English because case endings show grammatical relationships. This means the sentence could be rearranged in other ways, but the given order sounds very natural and easy to follow:

• scene first
• main action
• contrast

So the sentence flows like: After the rain, the children..., but the dog...

It can be understood as either, because Polish does not mark the difference with an article.

So po deszczu can mean:

• after the rain
• after rain
• once the rain is over

English translation depends on context. In a standalone sentence like this, after the rain is often the most natural choice.