Na stolu su jaja i povrće za večeru.

Because na can take different cases depending on meaning.

• na + locative = location, meaning on or at
• na + accusative = movement onto something

Here, the eggs and vegetables are already on the table, so Serbian uses the locative:

• sto = table
• stolu = on the table / at the table (locative singular)

Compare:

• Knjiga je na stolu. = The book is on the table.
• Stavljam knjigu na sto. = I am putting the book onto the table.

So na stolu is correct because this sentence describes a position, not motion.

Because su is a short form of the verb biti (to be) and it behaves like a clitic in Serbian. Clitics usually appear in the second position of the sentence or clause.

So in:

Na stolu su jaja i povrće za večeru.

the first unit is Na stolu, and then the clitic su comes right after it.

This word order is very natural in Serbian. You can also say:

Jaja i povrće su na stolu.

That is also correct, but it puts the focus a little differently. The original sentence starts with the location: On the table...

Because the subject is effectively jaja i povrće — eggs and vegetables — which is a coordinated plural idea.

Even though povrće is grammatically singular in form, jaja i povrće together form a plural subject, so Serbian uses the plural verb:

• su = are

Compare:

• Jaja su na stolu. = The eggs are on the table.
• Povrće je na stolu. = The vegetables/vegetable stuff is on the table.
• Jaja i povrće su na stolu. = The eggs and vegetables are on the table.

Yes. Jaja is the plural of jaje (egg).

This is normal for many neuter nouns in Serbian:

• jaje = egg
• jaja = eggs

So even though -a may remind an English speaker of singular feminine nouns, here it is a neuter plural form.

A few examples:

• jedno jaje = one egg
• dva jaja = two eggs
• Jaja su sveža. = The eggs are fresh.

Grammatically, povrće is usually treated as a singular neuter mass/collective noun.

It means vegetables in a general, uncountable sense, similar to English furniture or fruit in some contexts.

So by itself, it normally takes singular agreement:

• Povrće je na stolu. = The vegetables are on the table.

But when combined with another noun, as in jaja i povrće, the whole subject becomes plural, so the verb becomes su.

If you want to talk about individual vegetables, Serbian often uses specific nouns like:

• šargarepe = carrots
• paprike = peppers
• paradajz = tomatoes

Večeru is accusative singular of večera (dinner / supper).

The preposition za often takes the accusative, and one common meaning is for, especially in the sense of intended for or for use at a meal/time/event.

So:

• za večeru = for dinner

Examples:

• Šta imamo za večeru? = What are we having for dinner?
• Kupio sam ribu za večeru. = I bought fish for dinner.

So in your sentence, za večeru tells us what the eggs and vegetables are intended for.

Normally, it is understood to describe the whole phrase jaja i povrće.

So the natural reading is:

The eggs and vegetables are on the table for dinner.

In other words, both are part of dinner.

In real-life speech, context decides everything, but without special emphasis, most speakers will take za večeru as applying to the whole coordinated phrase, not just the second noun.

If someone wanted to make it clearer that only the vegetables were for dinner, they would usually rephrase the sentence.

Because Serbian has no articles.

English requires things like the table, the eggs, or some vegetables, but Serbian usually leaves that information to context.

So:

• sto can mean a table or the table
• jaja can mean eggs or the eggs
• povrće can mean vegetables, the vegetables, or some vegetables

The listener figures it out from the situation.

That is why Na stolu su jaja i povrće za večeru sounds complete without any article words.

It can change. Serbian word order is fairly flexible, although not completely free. Different word orders can sound more natural in different contexts and can shift the emphasis.

For example:

• Na stolu su jaja i povrće za večeru.
  Emphasis starts with the location: On the table...

• Jaja i povrće su na stolu.
  More neutral if you are talking about the eggs and vegetables themselves.

• Za večeru su na stolu jaja i povrće.
  Possible, but more marked; it emphasizes for dinner.

So the original version is very natural if the speaker is first pointing out where the items are.

In standard Serbian, not here. The verb su is needed.

Serbian can omit subjects because the verb ending already shows person and number, but it does not normally omit the present-tense form of to be in ordinary statements like this.

So:

• Na stolu su jaja i povrće. = correct
• Na stolu jaja i povrće. = not a normal full sentence in standard Serbian

You might see omissions in headlines, notes, or very informal fragments, but for normal grammar, su stays.

In Serbian, sentences of this type often work like English there is/there are sentences, even though Serbian does not need a separate dummy word like there.

So:

• Na stolu su jaja.
  can be understood as There are eggs on the table.

Literally, the structure is more like:

• On the table are eggs.

English usually prefers There are eggs on the table, but Serbian often starts with the location and then gives the things located there.

So the Serbian sentence naturally expresses both:

• location
• existence/presence in that location

That is one reason why this word order is so common.