A kabát gyorsan szárad, ha nyitva van az ablak.

Hungarian uses the definite article a / az very often, including in general statements where English may or may not use the.

• a kabát = the coat
• az ablak = the window

Here, a kabát gyorsan szárad can sound like the coat dries quickly or a general statement about the coat in question. Hungarian is often more comfortable using the article than English is.

Also, a and az are the same word; the form depends on the next sound:

• a kabát
• az ablak

Use az before a vowel sound, a before a consonant sound.

Because gyorsan is an adverb, meaning quickly, while gyors is an adjective, meaning quick or fast.

• gyors kabát = a fast/quick coat (which usually would not make much sense)
• gyorsan szárad = dries quickly

A very common pattern in Hungarian is:

• adjective: gyors = quick
• adverb: gyorsan = quickly

So the -an / -en / -on / -ön ending often turns an adjective into an adverb.

Szárad means to dry in the sense of becoming dry. It is usually intransitive.

• A kabát szárad. = The coat is drying / The coat dries.

By contrast, szárít means to dry something, so it is transitive.

• Szárítom a kabátot. = I am drying the coat.

So:

• szárad = the subject itself becomes dry
• szárít = someone causes something else to become dry

In your sentence, the coat itself is drying, so szárad is the correct choice.

Kabát is the subject here, not the object, so it stays in its basic form.

• A kabát gyorsan szárad.
  Here a kabát is the thing doing the drying, so it is the subject.

If it were an object, it would take the accusative ending -t:

• Szárítom a kabátot. = I’m drying the coat.

So compare:

• kabát = subject form
• kabátot = object form

Ha means if.

So:

• ha nyitva van az ablak = if the window is open

It introduces a condition, just like English if.

This structure is very common:

• Ha esik, nem megyünk. = If it rains, we aren’t going.
• Ha nyitva van az ablak, a kabát gyorsan szárad. = If the window is open, the coat dries quickly.

Both can be correct, but they are not exactly the same in feel.

• Az ablak nyitva van. = The window is open.
• Az ablak nyitott. = The window is open.

The structure nyitva van focuses on the state resulting from being opened. It is extremely common in everyday Hungarian.

• nyitva comes from the -va/-ve form
• van is is

So literally it is something like the window is in an opened state

This pattern is very common:

• Az ajtó csukva van. = The door is shut.
• A bolt zárva van. = The shop is closed.

For a learner, nyitva van is a very useful set phrase to remember.

Nyitva is a special verb form made with -va/-ve. In this sentence it expresses a state: open.

It comes from the verb nyit = to open.

So:

• nyit = open
• nyitva = opened/open, in an open state

In practice, learners often treat forms like these as fixed expressions:

• nyitva van = is open
• zárva van = is closed
• csukva van = is shut
• törve van = is broken

You do not need to translate it word-for-word every time. It is best learned as a common Hungarian structure.

That is a very good question. Hungarian often omits van in the present tense with nouns and adjectives:

• A kabát drága. = The coat is expensive.
• Az ablak nyitott. = The window is open.

But with forms like nyitva, zárva, csukva, Hungarian normally uses van:

• Az ablak nyitva van.
• Az ajtó csukva van.

So although Hungarian often drops is, it does not usually drop it in this -va/-ve + van structure.

Both are possible, but the word order changes the focus slightly.

• az ablak nyitva van = a more straightforward the window is open
• nyitva van az ablak = puts a bit more attention on being open

After ha, Hungarian often uses flexible word order depending on what is being highlighted. In your sentence, ha nyitva van az ablak sounds natural and idiomatic.

So the sentence could also be:

• A kabát gyorsan szárad, ha az ablak nyitva van.

That would still be correct.

It means if the window is open.

That is because nyitva van describes a state, not the action of opening.

If you wanted if someone opens the window, you would use a verb meaning opens:

• ha kinyitják az ablakot = if they open the window
• ha kinyitod az ablakot = if you open the window

So:

• nyitva van az ablak = the window is open
• kinyitják az ablakot = they open the window

Yes, but the nuance is slightly different.

• gyorsan szárad = dries quickly
• hamar szárad = dries soon / dries fast / dries in a short time

In many contexts they are close, and both can sound natural. But:

• gyorsan focuses more on the speed of the process
• hamar often focuses more on how soon the result happens

For many everyday situations, either one may work, but gyorsan szárad is perfectly natural here.

Yes, absolutely.

Hungarian allows this very naturally:

• A kabát gyorsan szárad, ha nyitva van az ablak.
• Ha nyitva van az ablak, a kabát gyorsan szárad.

Both mean the same thing. The difference is mainly in emphasis and flow:

• starting with A kabát... puts the coat first
• starting with Ha... puts the condition first

Both are good Hungarian.