Nawet kiedy piłkarz przegra ważny mecz, powinien dalej walczyć i trenować.

Kiedy means when. Adding nawet gives the idea of even when.

So:

• kiedy piłkarz przegra ważny mecz = when a footballer loses an important match
• nawet kiedy piłkarz przegra ważny mecz = even when a footballer loses an important match

The word nawet makes the sentence stronger: it says the advice still applies in a difficult situation.

Because przegra is the correct form for a future completed event with a perfective verb.

Here is the contrast:

• przegrał = he lost → past
• przegrywa = he is losing / he loses habitually → imperfective present
• przegra = he will lose / when he loses → perfective form with future meaning

In Polish, perfective verbs do not normally have a true present-tense meaning. Their “present-looking” forms often refer to the future.

So in this sentence:

• kiedy piłkarz przegra ważny mecz = when a footballer loses an important match

It refers to a situation that may happen, not to something already finished in the past.

These are an aspect pair:

• przegrać = to lose in a completed, single-result sense
• przegrywać = to be losing / to lose repeatedly / to lose in an ongoing sense

So:

• przegra mecz = he will lose the match / he loses the match
• przegrywa mecz = he is losing the match, or he loses matches in general

In your sentence, the speaker means a specific completed result: the footballer ends up losing an important match. That is why przegra is used.

Because mecz is the direct object of przegra, so it is in the accusative case. But mecz is a masculine inanimate noun, and in the singular its accusative form is the same as the nominative.

So:

• nominative: ważny mecz
• accusative: ważny mecz

That is why the form does not change.

Compare that with a masculine animate noun:

• nominative: dobry piłkarz
• accusative: dobrego piłkarza

So the lack of change in ważny mecz is normal.

Because Polish has no articles.

English needs words like a and the, but Polish does not. Polish usually shows definiteness from:

• context
• word order
• stress/emphasis
• the general meaning of the sentence

So piłkarz can mean:

• a footballer
• the footballer
• sometimes even footballers in general, depending on context

In this sentence, English most naturally uses a footballer because it sounds like a general statement.

Powinien means should or ought to.

It changes to match the gender and number of the subject:

• on powinien = he should
• ona powinna = she should
• oni powinni = they should (masculine personal)
• one powinny = they should (non-masculine-personal)

So in your sentence:

• piłkarz ... powinien = a footballer ... should

It is one of the main ways Polish expresses obligation or advice.

Because after powinien, Polish normally uses the infinitive.

So:

• powinien walczyć = should fight
• powinien trenować = should train

You do not need a second finite verb here. The same subject is understood for both infinitives.

That is why:

• powinien dalej walczyć i trenować

means:

• should keep fighting and training

Here dalej means further only in a very literal sense, but the natural English meaning is:

• still
• on
• continue to
• keep

So:

• dalej walczyć i trenować = keep fighting and training
• or continue fighting and training

It shows that the action should not stop, even after a setback.

Because Nawet kiedy piłkarz przegra ważny mecz is a subordinate clause, and Polish normally separates such clauses with a comma.

So the structure is:

• subordinate clause: Nawet kiedy piłkarz przegra ważny mecz
• main clause: powinien dalej walczyć i trenować

Polish commas are often more obligatory than English ones in this kind of sentence.

Yes, usually you can.

• kiedy = when
• gdy = also when

In this sentence, gdy would sound slightly more literary or formal to some speakers, but it is perfectly natural:

• Nawet gdy piłkarz przegra ważny mecz, powinien dalej walczyć i trenować.

The meaning stays basically the same.

Yes. Polish word order is flexible, though the emphasis changes.

For example:

• Nawet kiedy piłkarz przegra ważny mecz, powinien dalej walczyć i trenować.
• Piłkarz powinien dalej walczyć i trenować, nawet kiedy przegra ważny mecz.

Both are grammatical.

The original version emphasizes the difficult situation first: even when he loses an important match...

The second version starts with the main message: a footballer should keep fighting and training...

So the word order can move, but the speaker’s focus changes slightly.