Możemy zacząć wymianę ubrań, byleby ubrania nie miały przetarć.

Byleby means as long as, provided that, or so long as.

It introduces a condition that must be met:

• Możemy zacząć wymianę ubrań = we can start the clothing exchange
• byleby ubrania nie miały przetarć = as long as the clothes do not have worn spots

It is a very common Polish way to express a condition. A more formal alternative would be pod warunkiem że.

After byleby, Polish normally uses a verb form that looks like the past tense, but here it does not mean past time.

So:

• mają = they have
• miały = a form used here after byleby to express a condition

Also, ubrania is a non-masculine plural noun, so the correct plural form is miały, not mieli.

So byleby ubrania nie miały przetarć means as long as the clothes don't have any worn spots, not as long as the clothes didn't have...

Because wymianę is the accusative singular form, and it is the direct object of zacząć.

You ask:

• zacząć co? = to start what?
• wymianę

The dictionary form is wymiana. In this sentence, it changes to wymianę because of its grammatical role.

Because they are doing two different jobs, so they appear in two different cases.

• wymianę ubrań = exchange of clothes
  Here ubrań is genitive plural, because wymiana is followed by the thing being exchanged.

• ubrania nie miały przetarć = the clothes did not have worn spots
  Here ubrania is nominative plural, because it is the subject of miały.

So it is the same noun, but in different case forms.

It is plural.

• singular: ubranie
• plural: ubrania

This can be confusing because -a often looks singular to English speakers, but many Polish neuter plural nouns end in -a.

In this sentence, ubrania means clothes or garments.

Przetarć is the genitive plural form of przetarcie.

That happens because Polish usually uses the genitive after negated mieć:

• mieć przetarcia = to have worn spots
• nie mieć przetarć = to not have worn spots

So:

• ubrania nie miały przetarć = the clothes had no worn spots

This is a very common Polish pattern with negation.

Przetarcie is a worn, rubbed, or scuffed area caused by friction.

With clothes, it usually means:

• worn patches
• thinning fabric
• rubbed spots
• scuffed or abraded areas

It does not always mean a full hole. A full hole would more clearly be dziura.

So przetarcia suggests visible wear and tear.

No. Here wymiana ubrań means an exchange or swap of clothes.

So it is something like:

• a clothing exchange
• a clothes swap

If you want to say changing clothes, Polish would more often use:

• przebieranie się
• sometimes zmiana ubrań, depending on context

So wymiana is about exchanging one thing for another, not simply putting on different clothes.

Zacząć is perfective, while zaczynać is imperfective.

Here, zacząć is natural because the sentence is about a single action of beginning:

• Możemy zacząć = we can start / we can begin now

Polish often prefers the perfective verb when talking about a one-time completed beginning of an action.

Using zaczynać here would sound less natural unless you were talking about the process in a more general way.

Yes. Polish word order is flexible.

For example, you could also say:

• Byleby ubrania nie miały przetarć, możemy zacząć wymianę ubrań.

That means the same thing.

The original version is natural because it gives the main statement first and then adds the condition.

Because byleby ubrania nie miały przetarć is a subordinate clause.

In Polish, subordinate clauses introduced by words like byleby, żeby, jeśli, or ponieważ are normally separated by a comma.

So the comma here is standard and expected.