Kad bi publika tražila bis, glavni izvođač bi ostao.

Kad bi introduces a hypothetical situation: if / if ever / were to.

So in this sentence, Kad bi publika tražila bis... means something like:

• If the audience asked for an encore...
• If the audience were to ask for an encore...

By contrast, plain kad usually means when in a more real or expected sense:

• Kad publika traži bis, glavni izvođač ostaje.
  When the audience asks for an encore, the main performer stays.

So kad bi signals unreality, possibility, or imagination, not a normal repeated event.

Because Croatian often uses bi in both parts of this kind of conditional sentence:

• Kad bi publika tražila bis,
• glavni izvođač bi ostao.

This is the usual way to form the conditional:

• in the if-clause
• and in the main/result clause

English often does something similar with forms like:

• If the audience asked... the performer would stay.

So the two bi forms are normal and expected here.

They are very close, and in many contexts both are possible.

• Ako bi = if
• Kad bi = often if in hypothetical contexts, but literally comes from when

In real usage:

• Ako bi publika tražila bis, glavni izvođač bi ostao.
• Kad bi publika tražila bis, glavni izvođač bi ostao.

Both can mean essentially the same thing here.

A rough nuance:

• ako bi sounds more directly conditional: if
• kad bi can sound a bit more like if ever / were to / in the event that

But learners should know that both are common, and the difference is often small.

Because publika is a singular feminine noun in Croatian, even though it refers to a group of people.

So the verb agrees with the grammatical form of the noun, not with the fact that it contains many individuals.

• publika = singular feminine
• therefore: tražila

Compare:

• Publika je bila glasna.
• Publika je tražila bis.

Even though English may treat words like audience as sometimes singular or plural depending on dialect, Croatian normally treats publika as singular.

Because ostao agrees with glavni izvođač, which is masculine singular.

• izvođač = masculine singular
• so the past participle in the conditional is ostao

If the subject were feminine, it would change:

• glavna izvođačica bi ostala

This is part of a very important Croatian pattern: in forms like the past tense and the conditional, the participle agrees with the subject in gender and number.

Glavni is an adjective meaning main / principal / lead, and it must agree with the noun it describes.

Here:

• izvođač = masculine singular
• so the adjective is also masculine singular: glavni

If the noun changed, the adjective would change too:

• glavna izvođačica = main female performer
• glavni izvođači = main performers
• glavne izvođačice = main female performers

So glavni izvođač is a standard example of adjective-noun agreement.

Here bis is in the accusative singular, because it is the direct object of tražila.

• tražiti što? → bis

The reason it looks unchanged is that some masculine nouns, especially loanwords like bis, can have the same form in the nominative and accusative singular.

So:

• nominative: bis
• accusative: bis

This is completely normal here.

Also, tražiti bis is a common expression meaning to call for an encore.

Good question. Croatian aspect matters here.

• tražiti = imperfective, to ask for / to be asking for
• zatražiti = perfective, to request / ask for once, as a completed act

In this sentence, tražila sounds natural because it presents the action in a more general hypothetical way:

• If the audience asked for an encore...

You could also hear zatražila in some contexts, but it would feel a bit more focused on the request as a single completed act:

• Kad bi publika zatražila bis, glavni izvođač bi ostao.

Both can work, but tražila bis is very idiomatic and natural.

They look like past-tense forms, but in this sentence they are part of the conditional.

Croatian conditional is built with:

• the particle bi
• plus the past participle

So:

• bi tražila
• bi ostao

This does not mean simple past here. It means something hypothetical, equivalent to English would or would ... if structures.

So the sentence is not saying the audience actually asked and the performer actually stayed. It describes a possible or imagined situation.

Yes. Croatian word order is fairly flexible, and that version is also correct:

• Glavni izvođač bi ostao kad bi publika tražila bis.

Both mean the same thing. The difference is mainly one of focus or style.

• Kad bi publika tražila bis, glavni izvođač bi ostao.
  Focuses first on the condition.
• Glavni izvođač bi ostao kad bi publika tražila bis.
  Focuses first on the result.

However, the position of bi is not completely free. It usually goes in the second position of its clause, following the common clitic-placement rules of Croatian.

Because Croatian has no articles like English a/an/the.

So Croatian simply says:

• publika
• glavni izvođač

The meaning of the or a is understood from context.

That means a Croatian learner of English has to learn articles, but an English speaker learning Croatian has to get used to not using them at all.