Learn Hardcore Croatian: On želi letjeti iznad grada.

Both sentences are grammatically correct.
You usually include On to emphasize who you are talking about (e.g. contrast: On želi letjeti, ali ona ne želi – He wants to fly, but she doesn’t).

What is the difference between on and ona in a sentence like this?

On means he, and ona means she. The verb form here (želi) is the same for both:

On želi letjeti iznad grada. – He wants to fly above the city.
Ona želi letjeti iznad grada. – She wants to fly above the city.

Croatian verbs in the present tense do not change for gender, only for person and number. Gender is shown by the pronoun (or by context, if you drop the pronoun).

Why is it želi and not something like želim or žele?

The verb željeti (to want) is conjugated in the present tense. Here the subject is on (he), so you need the 3rd person singular form:

ja želim – I want
ti želiš – you (sg.) want
on / ona / ono želi – he / she / it wants
mi želimo – we want
vi želite – you (pl./formal) want
oni / one / ona žele – they want

So in this sentence, želi matches on.

Why is letjeti in the infinitive form? Could it be leti instead?

After verbs like željeti (to want), morati (must), moći (can), Croatian normally uses the infinitive of the second verb:

On želi letjeti. – He wants to fly.

Leti is the 3rd person singular present form of letjeti:

On leti iznad grada. – He is flying / He flies above the city.

So:

On želi letjeti iznad grada. – He wants to fly above the city (wanting).
On leti iznad grada. – He is flying above the city (actually flying now / generally).

How does iznad work here, and why is it grada and not grad?

Iznad is a preposition meaning above / over and it always takes the genitive case.
The noun grad (city) in the genitive singular becomes grada.

Nominative (dictionary form):

grad – city

Genitive singular:

grada – of the city

So:

iznad grada – above the city
Literally: above of‑the‑city, which is why grad changes to grada.

What is the difference between iznad and nad?

Both iznad and nad can mean above / over and both normally take the genitive:

iznad grada – above the city
nad gradom – above the city

Subtle differences:

iznad often suggests a bit more distance or a more abstract “higher than” (e.g. iznad prosjeka – above average).
nad is often used for something directly over/above or in fixed expressions (e.g. most nad rijekom – a bridge over the river).

In many concrete, physical contexts like this sentence, both are possible, but iznad grada is very common.

Could the word order be different, like On želi iznad grada letjeti?

Yes, Croatian word order is relatively flexible, though some variants sound more natural than others.

Most neutral: On želi letjeti iznad grada.
Possible, with a bit of emphasis on where: On želi letjeti iznad grada. (already natural)
On želi iznad grada letjeti. – grammatically OK, but sounds more marked/poetic or like you are emphasizing iznad grada.

You normally keep želi + infinitive (letjeti) together and put place expressions like iznad grada after the verb phrase.

How would I make this sentence negative?

To make it negative, add ne in front of the verb:

On ne želi letjeti iznad grada. – He does not want to fly above the city.

The structure is:

on (he) + ne želi (does not want) + letjeti (to fly) + iznad grada (above the city).

Is there any difference in meaning between On želi letjeti iznad grada and On hoće letjeti iznad grada?

Both željeti and htjeti can translate as to want, but there is a nuance:

On želi letjeti iznad grada. – He wants to fly above the city.
- Sounds a bit more neutral/polite, often used for wishes, desires.
On hoće letjeti iznad grada. – He wants / insists on flying above the city.
- Can sound slightly more insistent, stubborn, or more colloquial, depending on tone.

In many contexts they overlap, but željeti is generally safer and more neutral.

Does this sentence talk about the present or the future?

Grammatically, želi is the present tense: he wants (now).

However, what he wants is an action that will likely happen in the future (to fly above the city). So the sentence usually means:

Right now, he has the desire to fly above the city (at some time, probably in the future).

If you want to be very explicitly future, you can say, for example:

On želi da jednog dana leti iznad grada. – He wants to fly above the city one day.

Why is there no word for the in grada? How do I know it’s “the city” and not “a city”?

Croatian has no articles (no “a/an” or “the”). The noun form grada simply means of city; whether that is the city or a city is decided by context, not by a separate word.

So iznad grada can mean:

above the city (a specific, known city)
or
above a city (some unspecified city),

depending on what has been mentioned or is understood in the conversation.