Účastníci vyměnili sportovní vybavení a darovali oblečení.

Účastníci is the nominative plural form of účastník (participant).

It is in the nominative because it is the subject of the sentence — the people doing the actions.

• singular: účastník = participant
• plural: účastníci = participants

This noun is masculine animate, which matters for plural endings and verb agreement.

Both verbs are in the past tense, and they agree with the subject Účastníci, which is masculine animate plural.

In Czech past tense, masculine animate plural subjects usually give verbs the ending -i:

• účastníci vyměnili
• účastníci darovali

Compare:

• masculine animate plural: muži přišli
• feminine plural: ženy přišly
• neuter plural: města rostla

So the -i tells you the subject is plural masculine animate.

Because Czech often omits subject pronouns when the subject is already clear.

Here, Účastníci already tells you who did the action, so there is no need to add oni (they).

Czech commonly does this:

• Účastníci vyměnili... = The participants exchanged...
• Oni vyměnili... would be possible, but usually only if you want emphasis or contrast.

Because vybavení is often a singular collective/mass noun in Czech, even when English uses a plural idea like equipment.

So:

• vybavení = equipment
• not usually vybavení in the sense of countable equipments (English also normally does not say equipments)

Here sportovní vybavení means sports equipment as a general category, not necessarily one single item.

It is the accusative, because it is the direct object of vyměnili.

They exchanged what? → sportovní vybavení

However, vybavení is a neuter singular noun, and for many neuter nouns the nominative and accusative look the same. So even though the form does not change, its role in the sentence is accusative.

Also, sportovní matches vybavení in gender, number, and case.

Like vybavení, oblečení is often treated as a collective or mass noun in Czech.

So Czech says:

• darovali oblečení = donated clothing / donated clothes

Even though English often uses plural clothes, Czech commonly uses singular oblečení for clothing in general.

It is also in the accusative, because it is the direct object of darovali.

They donated what? → oblečení

Again, the form looks the same as nominative because oblečení is a neuter noun whose nominative and accusative are identical.

A simply means and.

It joins two actions done by the same subject:

• vyměnili sportovní vybavení
• darovali oblečení

So the sentence has one subject (Účastníci) and two coordinated verbs.

This is a question of aspect, which is very important in Czech.

• vyměnili = perfective
  It presents the action as completed.
• vyměňovali = imperfective
  It presents the action as ongoing, repeated, or viewed as a process.

So:

• Účastníci vyměnili sportovní vybavení.
  = They exchanged the sports equipment / they completed the exchange.
• Účastníci vyměňovali sportovní vybavení.
  = They were exchanging sports equipment / they used to exchange it / the action is viewed as a process.

In this sentence, the completed-event meaning is why vyměnili is used.

Yes. Darovali comes from darovat, which is typically used as a perfective verb meaning to give as a gift / to donate in a completed sense.

Here it tells us that the donation happened as a finished action.

So both verbs in the sentence describe completed actions:

• vyměnili
• darovali

Yes. Czech word order is fairly flexible, because grammatical roles are often shown by endings rather than position.

The neutral order here is very natural:

• Účastníci vyměnili sportovní vybavení a darovali oblečení.

But other orders are possible for emphasis, for example:

• Sportovní vybavení účastníci vyměnili a oblečení darovali.

That sounds more marked and would emphasize the objects. So the original sentence is probably the most neutral and natural version.

In this sentence, it is simplest to understand vyměnit as to exchange / swap.

Czech can also specify what something is exchanged for, often with za:

• vyměnit něco za něco = to exchange something for something

But here no second item is mentioned, so the sentence just says that the participants exchanged sports equipment.

A rough pronunciation guide is:

Účastníci ≈ OO-chaast-nyi-tsi

A few helpful points:

• ú = a long oo
• č = ch as in church
• á = a long a
• ní contains ň, a soft n sound, somewhat like ny
• ci is pronounced tsi

Also remember that in Czech, the stress is usually on the first syllable:

Ú-častníci

Because Czech does not have articles like English a/an/the.

So:

• účastníci can mean participants or the participants
• oblečení can mean clothing, the clothing, or sometimes some clothing

The exact meaning depends on context. That is normal in Czech.

Yes, depending on context.

The verb darovat can mean:

• to donate
• to give as a gift
• to give away

So darovali oblečení could mean they donated clothing in a charity/event context, or more generally they gave away clothes. The surrounding context tells you which English wording sounds best.