U torbi su ključ i kišobran.

Because after u meaning in for a fixed location, Serbian uses the locative case.

• base form: torba = bag
• locative singular: torbi = in the bag

So:

• u torbi = in the bag

If you used torba, that would just be the dictionary form, not the correct form after u in this sentence.

It is locative singular.

The noun torba is feminine, and its locative singular form is torbi.

This is a very common pattern:

• škola → u školi
• soba → u sobi
• torba → u torbi

So the sentence begins with a prepositional phrase in the locative: u torbi.

No. U can take different cases depending on the meaning.

• u + locative = location, being in something
  
  • u torbi = in the bag
• u + accusative = movement into something
  
  • u torbu = into the bag

So:

• U torbi su ključ i kišobran. = They are already in the bag.
• Stavio sam ključ u torbu. = I put the key into the bag.

This location vs. movement contrast is very important in Serbian.

Because the subject is two things together: ključ i kišobran.

Even though each noun is singular by itself:

• ključ = key
• kišobran = umbrella

together they form a compound subject, so the verb is plural:

• je = is
• su = are

Compare:

• U torbi je ključ. = There is a key in the bag.
• U torbi su ključ i kišobran. = There are a key and an umbrella in the bag.

Because Serbian word order is more flexible than English, and su is a clitic, which usually goes near the second position in the sentence or clause.

In this sentence, the first unit is U torbi, so su comes right after it:

• U torbi su ključ i kišobran.

This is natural Serbian.

You can also say:

• Ključ i kišobran su u torbi.

That is also correct, but the focus is a little different.
The original sentence highlights the location first: In the bag, there are...

Yes. They are in the nominative, because they function as the subject of the sentence.

Their forms here are the basic dictionary forms:

• ključ
• kišobran

That is why they do not change in this sentence.

Because Serbian does not have articles like English a/an/the.

So:

• ključ can mean a key or the key
• kišobran can mean an umbrella or the umbrella

The exact meaning depends on context.

That is normal in Serbian, and learners have to get used to understanding definiteness from the situation instead of from an article.

Yes, absolutely.

Both are correct:

• U torbi su ključ i kišobran.
• Ključ i kišobran su u torbi.

The difference is mainly focus:

• U torbi su ključ i kišobran.
  Emphasizes where they are.
• Ključ i kišobran su u torbi.
  Emphasizes what is in the bag.

So the original version is a bit like presenting the contents of the bag.

Not very much grammatically. You could also say:

• U torbi su kišobran i ključ.

That would still be correct.

Usually, the item mentioned first gets a little more attention or feels slightly more prominent, but the basic meaning stays the same.

No, not in a normal standard sentence like this.

You need the verb:

• U torbi su ključ i kišobran.

Leaving out su would sound incomplete or incorrect in standard Serbian.

Yes, structurally that is a good way to think about it.

Because the sentence starts with the location U torbi, it has a slightly presentational feel, similar to English There are ... in the bag.

Of course, depending on context, it can still be understood as The key and the umbrella are in the bag. But the Serbian structure naturally introduces the location first and then tells you what is there.

A few sounds may stand out for an English speaker:

• ključ
  The č sounds like ch in church.
  Roughly: klyooch
• kišobran
  The š sounds like sh in shoe.
  Roughly: kee-SHO-bran
• torbi
  Roughly: TOR-bee

Also remember that Serbian spelling is very regular, so once you know the sound values, pronunciation becomes much easier than in English.