Na onoj vješalici vise moja jakna, tvoj šal i dvije mokre kape.

Because na can take different cases depending on meaning:

• na + locative = location, on / at
• na + accusative = direction, onto / to

Here the clothes are already there, so this is a location phrase: na onoj vješalici = on that hanger / coat rack.

If you were talking about movement, you would use accusative:

• Stavio sam jaknu na onu vješalicu. = I put the jacket onto that hanger.

Onoj means that and it agrees with vješalici.

The base demonstrative is usually given as:

• onaj = masculine
• ona = feminine
• ono = neuter

But Croatian words like this change for case, gender, and number. Since vješalica is feminine singular, and after na here we need the locative, the correct form is onoj.

Compare:

• ona vješalica = that hanger (subject form)
• na onoj vješalici = on that hanger

Because the subject is plural overall:

• moja jakna
• tvoj šal
• dvije mokre kape

That is a list of several things, so Croatian uses the 3rd person plural verb:

• vise = hang / are hanging

If there were only one thing, you would use visi:

• Moja jakna visi na vješalici. = My jacket is hanging on the hanger.

It can cover both ideas. Croatian does not have a separate obligatory continuous/progressive form like English are hanging.

So vise here can naturally be understood as:

• hang
• are hanging

In this sentence, English usually sounds more natural with are hanging because it describes a current scene.

They are the subject of the sentence, so learners can think of them as being in the subject form.

More specifically:

• moja jakna = nominative singular
• tvoj šal = nominative singular
• dvije mokre kape = the feminine form used after dvije; in practice it looks like the regular feminine plural form

The important thing to notice is that these are the things doing the action of hanging, so they function as the subject of the sentence.

Because kape comes from kapa, which is a feminine noun.

With two, Croatian distinguishes gender:

• dva for masculine and neuter
• dvije for feminine

So:

• dvije kape = two hats
• dva šala / dva kaputa = two scarves / two coats

Because mokre has to agree with kape.

Since kape is feminine plural in form here, the adjective must also be feminine plural:

• mokre kape = wet hats

Compare:

• mokri kaputi = wet coats (masculine plural)
• mokra kapa = wet hat (feminine singular)

Because Croatian possessives such as moj and tvoj behave much like adjectives. They must agree with the noun in gender, number, and case.

So here:

• moja jakna = my jacket
  (jakna is feminine singular)
• tvoj šal = your scarf
  (šal is masculine singular)

You will see the forms change in other contexts:

• mojoj jakni = to/on my jacket
• tvoga šala = of your scarf

Yes. Croatian word order is fairly flexible.

This sentence begins with the location for emphasis:

• Na onoj vješalici vise moja jakna, tvoj šal i dvije mokre kape.

A more English-like order would be:

• Moja jakna, tvoj šal i dvije mokre kape vise na onoj vješalici.

Both are correct. The original version puts more focus on where the items are.

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

Whether something is definite or indefinite is usually understood from:

• context
• word order
• demonstratives such as ovaj, taj, onaj

Here, onoj already gives you that, so the phrase is clearly definite:

• na onoj vješalici = on that hanger / coat rack

Without a demonstrative, na vješalici could mean on a hanger or on the hanger, depending on context.

It can mean things like:

• hanger
• coat rack
• coat stand

The exact English word depends on context. Since several items are hanging there, English may often prefer coat rack or coat stand, even though hanger is also a possible literal translation in some contexts.

No. They are completely different words.

• vise = (they) hang / are hanging
• više = more, or sometimes any longer / no longer depending on context

The difference is the letter:

• s in vise
• š in više

So this sentence definitely uses vise from the verb visjeti = to hang.