Kiedy już podpiszę wszystkie dokumenty, wrócę do domu i wyślę list z tym wnioskiem.

These are perfective verbs, and in Polish the simple present-looking form of a perfective verb refers to the future.

So:

• podpiszę = I will sign
• wrócę = I will return
• wyślę = I will send

Polish usually forms the future in two main ways:

1. Imperfective verb: with będę

   • będę podpisywać = I will be signing / I will sign
     This focuses more on the process or repeated action.

2. Perfective verb: simple form

   • podpiszę = I will sign
     This focuses on the action as a completed whole.

In this sentence, the speaker means completed actions: first signing everything, then going home, then sending the letter.

Here kiedy literally means when, but in this kind of sentence it often has the practical sense of once / after.

So:

• Kiedy już podpiszę wszystkie dokumenty...
  = When / Once I’ve signed all the documents...

It introduces a time clause: one action happens first, and then the main actions happen afterward.

So in natural English, depending on context, you might translate it as:

• When I’ve signed all the documents...
• Once I’ve signed all the documents...
• After I sign all the documents...

Już usually means already, but in this sentence it adds a sense like:

• once
• as soon as
• finally after that
• when I have already finished

So:

• Kiedy już podpiszę wszystkie dokumenty...
  suggests: when I’m done signing all the documents

It makes the completion of the first action feel more explicit.

Without już, the sentence would still be correct:

• Kiedy podpiszę wszystkie dokumenty, wrócę do domu...

But już makes it sound a bit more like once I’ve finished.

Because dokumenty is the direct object of podpiszę (sign what?), so it goes in the accusative plural.

• singular: dokument
• plural nominative: dokumenty
• plural accusative: dokumenty

For this noun, nominative plural and accusative plural happen to look the same.

Wszystkie agrees with dokumenty in case, number, and gender.

So:

• wszystkie dokumenty = all the documents

A useful point: because dokumenty are non-masculine-personal, wszystkie is the correct plural form.

Because the preposition do requires the genitive case.

So:

• dom = nominative
• domu = genitive

That is why Polish says:

• wrócę do domu = I will return home

This is a very common pattern:

• iść do sklepu = to go to the shop
• wracać do pracy = to return to work
• jechać do Polski = to go to Poland

After do, you generally expect the noun to be in the genitive.

After the preposition z meaning with, Polish normally uses the instrumental case.

So:

• ten wniosek = this application / this request / this motion
• instrumental singular: tym wnioskiem

That gives:

• z tym wnioskiem = with this application/request

Compare:

• z kolegą = with a friend
• z mamą = with mum
• z dokumentem = with the document

So tym wnioskiem is instrumental because of z.

Wniosek is a word with several possible meanings depending on context. Common translations are:

• application
• request
• petition
• motion (in formal/legal/administrative contexts)
• sometimes even conclusion/inference in other contexts

In your sentence, it most likely means something like an application or formal request.

So:

• list z tym wnioskiem
  probably means a letter containing this application/request or a letter together with this application

The exact English word depends on the broader situation.

It most naturally suggests a letter with this application/request, so either:

• the letter contains the request/application, or
• the letter is sent together with it

Polish z is broad and often just means with in a practical sense.

So this phrase can feel a little flexible in English:

• I’ll send a letter with this application
• I’ll send a letter containing this request
• I’ll send a letter together with this application

The exact interpretation depends on context.

Because Kiedy już podpiszę wszystkie dokumenty is a subordinate clause, and in Polish subordinate clauses are normally separated by a comma.

So the structure is:

• Kiedy już podpiszę wszystkie dokumenty,
  subordinate time clause
• wrócę do domu i wyślę list z tym wnioskiem.
  main clause

Polish uses commas more consistently than English in this kind of structure, so learners often need to pay attention to that.

Yes, Polish word order is fairly flexible, though some orders sound more natural than others.

The original sentence is very natural:

• Kiedy już podpiszę wszystkie dokumenty, wrócę do domu i wyślę list z tym wnioskiem.

You could also say:

• Wrócę do domu i wyślę list z tym wnioskiem, kiedy już podpiszę wszystkie dokumenty.

This still works, but the original order is more natural if you want to present the timeline clearly: first signing, then going home, then sending the letter.

You can also move już around a little, but that may slightly change emphasis.

Because some Polish verbs change their stem when conjugated.

Here the infinitive is:

• wysłać = to send out / to send

But the 1st person singular future form is:

• wyślę = I will send

This is just part of the verb’s conjugation pattern and needs to be learned as a form.

A few useful forms:

• wyślę = I will send
• wyślesz = you will send
• wyśle = he/she/it will send
• wyślemy = we will send
• wyślecie = you will send
• wyślą = they will send

So yes, it is a bit irregular-looking from an English learner’s point of view.

Because wrócę is perfective and means I will return as a completed event.

• wrócę = I will come back / return
• będę wracać = I will be returning / I will be on my way back / I will be returning repeatedly, depending on context

In this sentence, the speaker means a clear sequence of completed actions:

1. sign all the documents
2. return home
3. send the letter

So perfective wrócę fits much better than imperfective będę wracać.

In everyday Polish, many speakers do say jak in this kind of time meaning, especially in speech:

• Jak już podpiszę wszystkie dokumenty, wrócę do domu...

That can mean something like when / once I sign all the documents.

However, kiedy is clearer and more standard in careful or neutral Polish, especially for learners.

So:

• kiedy = safer, more standard choice
• jak = common in colloquial speech, but can also mean how, so learners should use it carefully

It is talking about one-time completed actions.

That is shown by the perfective verbs:

• podpiszę
• wrócę
• wyślę

The speaker is not describing a process in progress, but a sequence of finished steps.

A rough timeline is:

• first: I sign all the documents
• then: I return home
• then: I send the letter

So the sentence is very completion-focused.