Leúszom két kilométert, hacsak nem fulladok ki.

Not necessarily. In this sentence, leúszom is best understood as I swim/complete the distance by swimming.

The prefix le- often has a completive feel in Hungarian: it can suggest that the action is carried through to its endpoint. So:

• úszom két kilométert = I swim two kilometers
• leúszom két kilométert = I swim the two kilometers through / all the way / successfully

With distances, Hungarian often uses prefixes this way, even when there is no real idea of physical downward movement.

Because úszik is traditionally an -ik verb, and the standard 1st person singular form is úszom.

So:

• úszik = he/she swims
• úszom = I swim
• leúszom = I swim it / I complete it by swimming

In everyday speech, many Hungarians also say úszok, so you may hear both. But úszom is a very normal standard form.

A useful thing to know: here, the -om ending is not something you should over-interpret as a special object-marking clue. With -ik verbs, -om/-em in 1st person singular is just a normal pattern.

Because Hungarian often uses the accusative for measured extent, including distance.

So két kilométert literally has the accusative ending:

• két kilométer = two kilometers
• két kilométert = two kilometers (as the distance covered)

This is very common with time and distance expressions:

• alszom nyolc órát = I sleep for eight hours
• sétálok egy kilométert = I walk a kilometer
• futok öt kilométert = I run five kilometers

English does not mark this with a case ending, but Hungarian does.

Formally, it is present tense. But in Hungarian, the present tense is very often used with future meaning, especially when the event is planned, expected, or seen as a whole.

So depending on context, Leúszom két kilométert can mean:

• I swim two kilometers
• I’m going to swim two kilometers
• I’ll swim two kilometers

Hungarian does have a future construction with fog + infinitive, but it is not required here.

Because Hungarian usually drops subject pronouns when they are not needed.

The verb form already tells you the subject:

• leúszom = I swim / I will swim
• fulladok ki = I get out of breath

So én is usually omitted unless you want emphasis or contrast:

• Én leúszom két kilométert = I will swim two kilometers

That would sound more emphatic, like contrasting yourself with someone else.

Because hacsak nem is the normal fixed expression meaning unless.

It is best learned as a unit:

• hacsak nem = unless

Examples:

• Elmegyek, hacsak nem esik. = I’ll go unless it rains.
• Megveszem, hacsak nem túl drága. = I’ll buy it unless it’s too expensive.

Even though nem literally means not, in hacsak nem the whole expression functions like English unless. So learners should usually memorize it as one chunk rather than translating each word separately.

Because in Hungarian, when a verb with a prefix is negated, the prefix usually moves after the verb.

The basic positive form is:

• kifulladok = I get out of breath

But with negation:

• nem fulladok ki

That same word-order rule appears here after hacsak nem as well. Since nem is present, the prefix ki goes behind the verb.

This is a very important Hungarian pattern:

• megírom = I write it

• nem írom meg = I don’t write it

• bemegyek = I go in
• nem megyek be = I don’t go in

Here it means I get out of breath, I run out of energy, or I tire myself out physically.

So the sentence means something like:

• I’ll swim two kilometers, unless I get too out of breath.

This is not the same as megfulladok, which means I suffocate / choke / asphyxiate.

So:

• kifulladok = I get winded / exhausted
• megfulladok = I suffocate

That distinction is worth learning, because the English learner may notice the shared root and assume a much more dramatic meaning than intended.

Yes. Hungarian word order is flexible, and changing it usually changes emphasis rather than basic meaning.

The given sentence is a natural neutral version:

• Leúszom két kilométert, hacsak nem fulladok ki.

But you could also say:

• Hacsak nem fulladok ki, leúszom két kilométert.
  This puts the unless-clause first.

Or:

• Két kilométert leúszom, hacsak nem fulladok ki.
  This puts more emphasis on two kilometers.

So the original order is not the only possible one; it is simply a natural, unmarked way to say it.

Both can refer to swimming two kilometers, but leúszom sounds more like I complete the whole two kilometers.

Very roughly:

• úszom két kilométert = I swim two kilometers
• leúszom két kilométert = I get through / complete two kilometers by swimming

So the prefix le- adds a sense of boundedness or completion. In many real contexts, the difference is subtle, but it is still a useful nuance to notice.