Rozcvička začne, až zaplatíme vstupné.

Because začne comes from the verb začít (to begin/start), which is perfective.

In Czech, perfective verbs do not normally have a present meaning. Their “present-tense” forms are usually used for the future. So:

• začne = it will begin
• not it begins in the normal present-time sense

By contrast, začínat is the imperfective partner:

• začíná = it is beginning / it begins
• bude začínat = it will be beginning / it will start repeatedly or in a more process-oriented way

Here, the sentence talks about one completed future event, so začne is the natural choice.

For the same reason as začne: zaplatíme comes from zaplatit (to pay, perfective).

With perfective verbs, Czech uses present-tense forms to express a future completed action:

• zaplatíme = we will pay

So even though the form looks “present,” the meaning is future because the verb is perfective.

This is very common in Czech:

• udělám = I will do
• řekneš = you will say
• přijdou = they will come

Here až means something like:

• when
• once
• not until

In this sentence, the sense is:

• The warm-up will begin once we pay the admission fee
• or The warm-up will not begin until we pay the admission fee

So až introduces a time clause referring to a future moment.

A useful comparison:

• když = when in a more general or neutral sense
• až = when/once/not until, often pointing to a specific future threshold

In this sentence, až is the natural choice because paying is the condition/time point after which the main event happens.

Because až zaplatíme vstupné is a subordinate clause.

Czech normally separates subordinate clauses with a comma, including clauses introduced by words like:

• že = that
• když = when
• až = when/until
• protože = because

So:

• Rozcvička začne, až zaplatíme vstupné.

If you reverse the order, you also keep the comma:

• Až zaplatíme vstupné, rozcvička začne.

Yes. A very natural alternative is:

• Až zaplatíme vstupné, rozcvička začne.

This means the same thing.

The difference is mainly one of focus and flow:

• Rozcvička začne, až zaplatíme vstupné.
  starts with the main point: the warm-up will begin
• Až zaplatíme vstupné, rozcvička začne.
  starts with the time condition: once we pay

Both are correct and natural.

Because Czech often omits subject pronouns when they are already clear from the verb ending.

The ending -íme in zaplatíme tells you the subject is we.

So:

• zaplatíme = we will pay

You could say my zaplatíme, but that would usually add emphasis, something like:

• we will pay

In neutral sentences, Czech usually leaves pronouns out.

Začne is:

• 3rd person singular
• from začít
• perfective
• formally a present-tense form, but with future meaning

It matches rozcvička, which is singular:

• rozcvička začne = the warm-up will begin

If the subject were plural, the verb would change:

• Rozcvičky začnou. = The warm-ups will begin.

Here vstupné is the direct object of zaplatíme, so it is in the accusative.

But vstupné is a neuter noun, and for many neuter nouns the nominative and accusative forms are identical. So the form does not change.

That is why:

• vstupné can be nominative
• vstupné can also be accusative

In this sentence, it is accusative because it is the thing being paid.

Vstupné is a noun meaning:

• admission fee
• entrance fee
• ticket price (depending on context)

Historically, forms like this are related to adjectives, which is why they look adjective-like. But in modern usage, vstupné functions as a noun.

Examples:

• Zaplatili jsme vstupné. = We paid the admission fee.
• Vstupné je drahé. = The admission fee is expensive.

This is an aspect pair:

• začít = perfective
• začínat = imperfective

Very roughly:

• začít focuses on the moment of beginning, as a completed event
• začínat focuses more on the process, repetition, or ongoing nature

Examples:

• Rozcvička začne v deset. = The warm-up will begin at ten.
• Rozcvička začíná v deset. = The warm-up begins/is beginning at ten.

In your sentence, the speaker means one future event that will happen after another future event, so začít is the right choice.

Not quite.

It is mainly a time clause, not a true conditional clause.

• až zaplatíme vstupné = when/once we pay the admission fee
• jestli zaplatíme vstupné = if we pay the admission fee

So až suggests that the paying is expected to happen, and the warm-up begins after that point. Jestli would make it sound uncertain whether the payment happens at all.

Not naturally.

A more natural English translation would be:

• The warm-up will begin once we pay the admission fee.
• The warm-up will begin when we pay the admission fee.
• The warm-up won’t begin until we pay the admission fee.

The Czech verb forms look present in shape, but because they are perfective, they refer to the future. So English usually needs will here.

Yes, rozcvička is a feminine singular noun.

It matters because the verb agrees with it in number and person:

• rozcvička začne = singular
• if it were plural: rozcvičky začnou

Gender matters more clearly in adjectives and past tense forms, but it is still useful to know that rozcvička is feminine.