W razie gdyby rój był przy domu, pszczelarz sprawdzi ul.

It means something like in case, if it should happen that, or should ... in English.

• w razie = in case / in the event of
• gdyby = if / if ... were / should

Together, w razie gdyby sounds a bit more cautious and contingency-based than plain jeśli. It introduces a possible situation and then tells you what will be done if that situation happens.

So this sentence is not just a neutral if X, then Y. It is more like:

• In case the swarm is near the house, the beekeeper will check the hive.
• If the swarm should be near the house, the beekeeper will check the hive.

It may look redundant to an English speaker, but it is a normal Polish pattern.

• w razie sets up the idea of a contingency: in case of / in the event of
• gdyby introduces the clause with the hypothetical situation

So w razie gdyby rój był przy domu is a standard way to say in case the swarm should be near the house.

You could use just jeśli in many contexts, but w razie gdyby sounds more like planning for a possibility.

After gdyby, Polish normally uses the past-tense-like form of the verb, but here it does not mean real past time.

So był here does not mean simply was. In this structure, it means something more like:

• were
• should be
• happened to be

This is a very common Polish pattern:

• gdyby był = if he/it were / if he/it should be
• gdyby przyszła = if she came / if she should come
• gdyby padało = if it rained / if it should rain

So the -ł form after gdyby signals hypothesis, not past time.

Because after gdyby, Polish does not normally use the future form będzie.

The standard pattern is:

• gdyby + past-form

So:

• gdyby rój był = if the swarm were / should be

Not:

• gdyby rój będzie ✘

That would sound ungrammatical in standard Polish.

Rój is in the nominative singular because it is the subject of the subordinate clause.

In gdyby rój był przy domu:

• rój = the thing being talked about
• był agrees with rój

Since rój is masculine singular, the verb form is also masculine singular: był.

Przy takes the locative case, so dom becomes domu.

• dom = house
• przy domu = by the house / near the house

So the grammar is:

• przy + locative

This is different from:

• w domu = in the house
• do domu = to the house
• obok domu = next to the house

Here przy domu means the swarm is near or by the house, not inside it.

Ul is the direct object, so it is in the accusative case. But for many masculine inanimate singular nouns, the accusative form is the same as the nominative form.

So:

• nominative: ul
• accusative: ul

That is why it does not change.

Compare that with a masculine animate noun, where the accusative often changes:

• widzę psa = I see a dog

But:

• sprawdzi ul = will check the hive

This is because sprawdzić is a perfective verb.

In Polish, perfective verbs do not normally have a true present tense for ordinary meaning. Their present-looking forms are used to express the future.

So:

• sprawdzi = will check

Compare:

• sprawdza = checks / is checking
  imperfective, present
• sprawdzi = will check
  perfective, future

So although it looks like a present form on the surface, its meaning here is future.

Because sprawdzić is perfective and suggests one complete check.

So pszczelarz sprawdzi ul means:

• the beekeeper will check the hive
• the action will be completed as a single event

If you used the imperfective verb, the meaning would shift more toward process, repetition, or duration, for example:

• będzie sprawdzał ul = will be checking the hive / will check the hive for some time

So sprawdzi is the natural choice if you just mean one inspection.

Because Polish normally uses a comma to separate a subordinate clause from the main clause.

Here the subordinate clause comes first:

• W razie gdyby rój był przy domu, = subordinate clause
• pszczelarz sprawdzi ul. = main clause

So the comma is required.

The word order is fairly flexible, but the given order is natural because it puts the condition first.

This version:

• W razie gdyby rój był przy domu, pszczelarz sprawdzi ul.

first tells us the condition, then the result.

You could rearrange parts for emphasis, but not every variation sounds equally natural. For a learner, the given order is a very good neutral model.

No. Przy domu means by the house, near the house, or next to the house.

If you want at home in the sense of location inside one’s home or at one’s residence, Polish usually uses something like:

• w domu = at home / in the house

So:

• przy domu = near the house
• w domu = in the house / at home

That distinction matters here, because the sentence is talking about where the swarm is physically located.