Sve što moja rodbina želi za tu godišnjicu jest mirna večera i dovoljno vremena za razgovor.

This is a very common Croatian structure meaning All that ... is ... or, more naturally in English, All ... wants is ....

In this sentence:

• Sve što moja rodbina želi za tu godišnjicu = All that my relatives want for that anniversary
• jest mirna večera i dovoljno vremena za razgovor = is a quiet dinner and enough time to talk

So the whole sentence is built like:

All that X wants is Y.

Here što is not a question word. It is a relative pronoun.

In the expression sve što, it means everything that or all that.

So:

• sve što želi = everything that he/she wants
• sve što moja rodbina želi = everything that my relatives want

This is a fixed and very common pattern in Croatian.

Because rodbina is a collective noun. It refers to a group of people, but grammatically it is singular feminine.

That means it takes:

• singular adjective: moja rodbina
• singular verb: moja rodbina želi

This is similar to how English sometimes treats words like family or government as singular, depending on the variety of English.

Not exactly.

Rodbina usually means relatives, kin, or extended family.
If you want family in the sense of your immediate family or household, Croatian usually uses obitelj.

So moja rodbina is closer to my relatives than to my family.

Because za here means for, and in this meaning it takes the accusative.

The base form is:

• ta godišnjica = that anniversary (nominative)

In the accusative it becomes:

• tu godišnjicu

Both words change because godišnjica is feminine singular:

• ta → tu
• godišnjica → godišnjicu

So za tu godišnjicu means for that anniversary.

Jest is the full/stressed form of je.

In everyday speech, many speakers would simply say je:

• Sve što moja rodbina želi ... je ...

But jest often sounds:

• a bit more formal
• a bit more careful or literary
• sometimes slightly emphatic

So in this sentence, jest is perfectly natural, especially in writing.

Because the verb agrees with the subject, not with the list after it.

The subject here is the whole phrase:

Sve što moja rodbina želi za tu godišnjicu

Its head is sve, which is treated as singular. So the verb is singular:

• jest, not jesu

This is similar to English:

• All they want is a quiet dinner and enough time to talk.

Even though two things are listed, all is still singular in that structure.

Because after jest you normally use a predicate noun phrase, not a direct object.

So mirna večera is in the nominative, because it is what the subject is.

Compare:

• Moja rodbina želi mirnu večeru.
  Here mirnu večeru is the direct object of želi, so it is accusative.

• Sve što moja rodbina želi jest mirna večera.
  Here mirna večera is the complement after jest, so it is nominative.

Because words like dovoljno, puno, malo, mnogo, and dosta often take the genitive in Croatian.

So:

• dovoljno vremena = enough time
• puno ljudi = many people
• malo novca = little money

Here vremena is the genitive singular of vrijeme.

This is very natural Croatian. English does not show a case change here, but Croatian does.

Yes, that can exist, but it is not quite the same in feel.

• dovoljno vremena is the most idiomatic way to say enough time
• dovoljno vrijeme treats dovoljno more like an agreeing adjective meaning sufficient/adequate

In this sentence, dovoljno vremena is the more natural choice.

It is accusative singular after za.

The reason it looks unchanged is that razgovor is a masculine inanimate noun, and for many masculine inanimate nouns:

• nominative singular = accusative singular

So:

• nominative: razgovor
• accusative: razgovor

Here za razgovor means for conversation or more naturally to talk.

Yes. Croatian word order is flexible, and changing it changes the emphasis more than the basic meaning.

The given sentence puts strong focus on everything my relatives want:

Sve što moja rodbina želi za tu godišnjicu jest ...

A more neutral version might be:

Moja rodbina za tu godišnjicu želi samo mirnu večeru i dovoljno vremena za razgovor.

So the original wording sounds a bit more formal and stylistically shaped.

Yes, godišnjica is common and fully correct.

You may also see obljetnica, which is also very common in Croatian and is sometimes felt to be a bit more formal or more specifically standard-Croatian in tone.

So both are normal words, but this sentence uses godišnjica.