Wieczorem odpocznę, chyba że sąsiadka znowu poprosi mnie o pomoc z kartonami.

Wieczorem is a very common adverbial time expression meaning in the evening or sometimes this evening, depending on context.

It comes from wieczór = evening, but in this fixed form you do not usually translate it word for word. A native English speaker might expect something like w wieczór, but that is not how Polish normally says it.

So:

• Wieczorem odpocznę = I’ll rest in the evening / this evening

Odpocznę is the 1st person singular future of the perfective verb odpocząć.

That means the speaker is talking about a future action seen as a whole: I’ll rest / I’ll have a rest.

Compare:

• odpocznę = I will rest, viewed as one complete event
• będę odpoczywać = I will be resting, more focused on the process or duration
• odpoczywam = I am resting / I rest, present tense

So odpocznę is a natural choice here because the sentence is about a future plan.

Yes, this is one of those stem changes that learners simply have to get used to.

The infinitive is odpocząć, but in some conjugated forms the stem changes:

• odpocząć = infinitive
• odpocznę = I will rest
• odpocznie = he/she will rest

So although it may look surprising at first, odpocznę is the normal correct form.

Chyba że is a fixed expression meaning unless.

It introduces an exception to what was just said:

• Wieczorem odpocznę = I’ll rest in the evening
• chyba że... = unless...

So the whole structure is:

• I’ll rest in the evening, unless...

It is best learned as one chunk: chyba że = unless.

Because chyba że introduces a subordinate clause, and in Polish such clauses are normally separated by a comma.

So this is standard punctuation:

• Wieczorem odpocznę, chyba że...

The comma is not optional here in normal written Polish.

This is a very common source of confusion.

Poprosi comes from the perfective verb poprosić. Perfective verbs in Polish use forms that look like present tense, but their meaning is future.

So:

• poprosi = she will ask
• not she asks

Compare:

• prosi from imperfective prosić = she asks / she is asking
• poprosi from perfective poprosić = she will ask

So in this sentence:

• sąsiadka znowu poprosi mnie... = the neighbor will ask me again...

Because poprosić kogoś means to ask someone, and that someone is a direct object, so Polish uses the accusative.

The pronoun mnie is the accusative form of ja here.

• poprosi mnie = she will ask me

But mi is usually dative:

• da mi = will give me
• pomógł mi = he helped me

So in this sentence, mi would be wrong.

The verb pattern is:

• prosić / poprosić kogoś o coś = to ask someone for something

So after o in this pattern, Polish uses the accusative.

That gives:

• poprosi mnie o pomoc = she will ask me for help

A detail that can be confusing: pomoc looks the same in nominative and accusative, so the form does not visibly change here.

You can see the case more clearly with other nouns:

• prosić o kawę = ask for coffee
• prosić o radę = ask for advice

Here z means with, and after z in this meaning Polish uses the instrumental.

So:

• kartony = boxes / cartons nominative plural
• kartonami = instrumental plural

That gives:

• pomoc z kartonami = help with the boxes / help with the cartons

Be careful: z can also mean from, but then it usually takes the genitive, not the instrumental. So here it definitely means with, not from.

Yes. Sąsiadka is feminine, so it means female neighbor.

Compare:

• sąsiad = male neighbor
• sąsiadka = female neighbor

Also, Polish has no articles, so sąsiadka could be translated as:

• the neighbor
• a neighbor
• sometimes even my neighbor, if the context makes that clear

English has to choose, but Polish often leaves that to context.

Yes, Polish word order is flexible, though the original sentence sounds natural and neutral.

• sąsiadka znowu poprosi mnie... puts again in a natural position
• znowu sąsiadka poprosi mnie... can sound more like it’s the neighbor again who will ask me
• sąsiadka poprosi mnie znowu... is also possible, with slightly different emphasis

Likewise, the first part could also be:

• Odpocznę wieczorem...

But Wieczorem odpocznę... is perfectly normal and puts a little focus on the time: In the evening, I’ll rest...