Vrata su izvana mokra, ali iznutra su čista.

Because vrata is a plural-only noun in Croatian. Even when it refers to one door as a whole, it behaves grammatically as plural.

That is why the sentence uses:

• su = are
• mokra = plural adjective
• čista = plural adjective

So Croatian literally looks more like The door are wet on the outside..., but this is completely normal grammar.

It is in the nominative plural, because it is the subject of the sentence.

• Vrata = the thing being described
• su mokra / su čista = what is being said about it

So the basic structure is:

• Vrata su mokra.
• Vrata su čista.

Both use vrata as the subject.

They agree with vrata in gender, number, and case.

Since vrata is:

• neuter
• plural
• nominative

the predicate adjectives must also be neuter plural nominative:

• mokra
• čista

This is why they do not appear as:

• mokar / čist (masculine singular)
• mokra / čista feminine singular — even though the forms look the same in some cases

Here they are specifically neuter plural forms.

They mean:

• izvana = from the outside / on the outside / externally
• iznutra = from the inside / on the inside / internally

In this sentence, the most natural English sense is:

• on the outside
• on the inside

They are adverbs, so they do not change for case, gender, or number.

Because the sentence has two coordinated parts joined by ali:

• Vrata su izvana mokra
• ali iznutra su čista

Each part has its own implied structure with the verb biti (to be), so repeating su is standard and clear.

You may also hear a shorter version such as:

• Vrata su izvana mokra, ali iznutra čista.

But the full version with both su is very natural and especially clear for learners.

Because su is a clitic, and Croatian clitics normally go in the second position in their clause.

So:

• Vrata su izvana mokra.
  Here Vrata is first, so su comes second.

• ... ali iznutra su čista.
  Here iznutra is first in that clause, so su comes second.

This second-position behavior is very common in Croatian.

Sometimes yes, but izvana / iznutra is especially natural when talking about the outer side and inner side of something.

A rough distinction is:

• vani / unutra = outside / inside as a location
• izvana / iznutra = from the outside / from the inside, or on the outer/inner side

So for a door being wet on one side and clean on the other, izvana and iznutra fit very well.

No, Croatian word order is fairly flexible.

You could also say:

• Vrata su mokra izvana, ali čista iznutra.

That means basically the same thing. The original version:

• Vrata su izvana mokra, ali iznutra su čista.

puts izvana and iznutra in parallel positions, which nicely emphasizes the contrast between the outside and the inside.

So the original sounds balanced and natural.

Croatian does not have articles like English the or a/an.

So vrata can mean:

• the door
• a door
• sometimes doors, depending on context

The exact meaning is understood from the situation, context, and sometimes word order.

Because ali means but, and in Croatian it normally introduces a contrasting clause that is separated by a comma.

So:

• Vrata su izvana mokra, ali iznutra su čista.

This is similar to standard English punctuation with but in a sentence joining two full clauses.