Jeśli królik znowu ucieknie, będziemy go szukać na podwórku za domem.

Yes. Jeśli means if and introduces a condition, just like in English.

So:

• Jeśli królik znowu ucieknie = If the rabbit runs away again
• będziemy go szukać... = we will look for him...

A useful difference from English is that Polish does not change the word order the way English sometimes does. There is no equivalent of English-style inversion or special auxiliary movement. Polish simply keeps a normal clause after jeśli.

You can also reverse the clauses:

• Będziemy go szukać na podwórku za domem, jeśli królik znowu ucieknie.

Both versions are natural.

Because królik is the subject of ucieknie.

In this clause:

• królik = the rabbit
• ucieknie = will run away / escapes

Subjects normally appear in the nominative case, which is the dictionary form. So królik stays królik.

This is about aspect, which is one of the biggest topics in Polish.

• ucieknie is perfective
• uciekać is imperfective

Polish usually uses:

• perfective present-form endings to express a single future completed action
• będzie + infinitive for the future of imperfective verbs

So:

• ucieknie = will run away / runs away in the future sense
• będzie uciekać = will be running away / will keep escaping, depending on context

Here, the sentence means one complete event: the rabbit escapes again. That is why ucieknie is the natural choice.

Because with perfective verbs, forms that look like present tense actually refer to the future.

So for a perfective verb like uciec:

• ucieknę = I will run away
• uciekniesz = you will run away
• ucieknie = he/she/it will run away

Perfective verbs do not normally have a true present-tense meaning, because they describe actions seen as completed wholes. That is why ucieknie means will run away, not is running away.

Because szukać is imperfective, and its future is formed with będę, będziesz, będzie... + infinitive.

So:

• będziemy szukać = we will be looking / we will look for

This makes sense because searching is usually seen as a process, not a single completed moment.

There is a nice aspect contrast in the sentence:

• ucieknie = one completed event
• będziemy szukać = the activity that follows

That contrast is very natural in Polish.

Go means him/it and is the accusative form of the pronoun referring to królik.

Since szukać takes a direct object in the accusative, the rabbit becomes:

• go = him / it

So:

• będziemy go szukać = we will look for him/it

Because królik is grammatically masculine animate, Polish uses the masculine animate pronoun form go.

Both are possible, but go often appears before the infinitive or verb in neutral Polish word order.

So:

• będziemy go szukać = very natural
• będziemy szukać go = possible, but often sounds more marked, contrastive, or stylistically different

Polish pronouns like go, mi, ci, mu often prefer earlier positions in the clause. A learner will hear this a lot.

Because na can mean either:

• on/to a place with movement toward it
• on/at a place with location

Here the meaning is location:

• we will look for him at/in the yard

So Polish uses na + locative:

• na podwórku

Compare:

• Idę na podwórko. = I’m going into/out to the yard.
  
  • movement, so na + accusative
• Jestem na podwórku. = I’m in the yard / in the courtyard.
  
  • location, so na + locative

In your sentence, the searching happens there, so na podwórku is correct.

It is the locative singular of podwórko.

Basic form:

• podwórko = yard / courtyard

After na in a location meaning, it changes to locative:

• na podwórku

This is a very common pattern with neuter nouns ending in -o.

Because za changes case depending on meaning.

For location behind something, Polish uses:

• za + instrumental

So:

• za domem = behind the house

If there were motion to a place behind the house, Polish could use:

• za dom = to behind the house

But in this sentence, the yard is located behind the house, so the static-location form is needed:

• na podwórku za domem = in the yard behind the house

No, its position is somewhat flexible, although some placements sound more neutral than others.

In this sentence:

• Jeśli królik znowu ucieknie... = If the rabbit runs away again...

This is very natural.

You may also hear:

• Jeśli znowu królik ucieknie...
• Jeśli królik ucieknie znowu...

But those can sound more marked or may shift emphasis. The version in your sentence is a very good neutral choice.

Because Polish separates the conditional clause introduced by jeśli from the main clause with a comma.

So:

• Jeśli królik znowu ucieknie, będziemy go szukać...

This is standard punctuation.

The same happens if the main clause comes first:

• Będziemy go szukać na podwórku za domem, jeśli królik znowu ucieknie.

Yes. In fact, Polish usually does leave it out unless it is needed for emphasis or contrast.

• będziemy szukać already means we will look
• the ending -my tells you the subject is we

So:

• będziemy go szukać = normal
• my będziemy go szukać = we will look for him, with extra emphasis or contrast

This is very common in Polish: subject pronouns are often omitted because the verb ending already gives the person and number.

Yes, but the meaning or nuance would change.

• szukać is imperfective: the process of looking/searching
• poszukać is perfective: to search for a while / to carry out a search as one bounded event

So:

• będziemy go szukać focuses on the activity
• poszukamy go or będziemy go szukać could both be possible in some contexts, but they are not identical

In your sentence, będziemy go szukać sounds natural because it presents the search as an ongoing action that will happen if the rabbit escapes.

Grammatically, królik is masculine, so Polish uses masculine pronoun forms:

• go = him/it

In English, an animal may be called it or he/she depending on context. Polish grammar, however, follows the noun’s grammatical gender much more consistently.

So even if English translation uses it, the Polish form is still:

• go

because królik is masculine.

A useful way to break it down is:

• Jeśli
  • subject + adverb + perfective future
• main clause with future of an imperfective verb
• object pronoun in accusative
• location phrases with the correct cases

So the structure is:

• Jeśli królik znowu ucieknie,
  conditional clause: if the rabbit runs away again
• będziemy go szukać
  main clause: we will look for him
• na podwórku za domem
  location: in the yard behind the house

This sentence is a very good example of several core Polish patterns working together:

• condition with jeśli
• aspect contrast
• omitted subject pronoun
• object pronoun placement
• locative after na
• instrumental after za for location