Azon kívül, hogy gyors az internetkapcsolat, a szkenner is elérhető.

It is a fixed expression meaning apart from the fact that..., besides the fact that..., or in addition to the fact that....

Here it introduces one fact first, and then adds another one:

• fact 1: the internet connection is fast
• fact 2: the scanner is also available

So the sentence is not talking about physical outside here; it is using kívül in an abstract sense.

Because kívül is used in a postposition-like expression, and with demonstratives Hungarian uses forms like ezen and azon.

So:

• ezen kívül = besides this
• azon kívül = besides that / apart from that

This is a normal pattern in Hungarian. A learner usually just has to memorize ezen kívül and azon kívül as common expressions.

Hogy means that and introduces a clause.

Compare:

• Azon kívül, hogy gyors az internetkapcsolat... = apart from the fact that the internet connection is fast...
• Azon kívül... without hogy would normally need a noun phrase, not a full clause.

So hogy is there because what follows is a complete statement: gyors az internetkapcsolat.

Both are grammatical, but the emphasis is slightly different.

• Gyors az internetkapcsolat puts more attention on gyors as the important information.
• Az internetkapcsolat gyors makes az internetkapcsolat more of the topic, and then says something about it.

Hungarian word order is strongly connected to information structure. In this sentence, gyors is presented as the key fact inside the subordinate clause.

In Hungarian, the present-tense copula van is usually omitted in the third person singular when the predicate is a noun or adjective.

So Hungarian says:

• gyors az internetkapcsolat = the internet connection is fast
• a szkenner elérhető = the scanner is available

But in other persons, or in past/future, a form of lenni appears:

• gyors vagyok = I am fast
• gyors volt = it was fast

It is a compound noun:

• internet
• kapcsolat = connection

So internetkapcsolat means internet connection.

Hungarian very often writes compounds as a single word when they form one lexical unit. That is much more common than in English.

A and az are just two forms of the same definite article, equivalent to the.

The choice depends on the following sound:

• az before a vowel sound: az internetkapcsolat
• a before a consonant sound: a szkenner

So this is similar to the English difference between a and an, except it applies to the definite article.

Is means also, too, or sometimes even, depending on context.

In Hungarian, is comes after the word or phrase it modifies. So:

• a szkenner is elérhető = the scanner too is available / the scanner is also available

If is were attached to another part of the sentence, the emphasis would change. Its position is very important.

Elérhető means available, accessible, or reachable.

It comes from:

• elér = to reach / to access
• -hető = a suffix meaning something like can be or able to be

So elérhető literally has the sense of can be reached/accessed. In this sentence, available or accessible is the most natural interpretation.

Because Hungarian separates subordinate clauses with commas.

Here, hogy gyors az internetkapcsolat is a subordinate clause introduced by hogy, and the main clause comes after it:

• subordinate part: Azon kívül, hogy gyors az internetkapcsolat
• main clause: a szkenner is elérhető

So the commas help mark that structure clearly.

Not if you want to keep exactly the same structure and meaning.

With hogy, you are referring to a whole fact:

• Azon kívül, hogy gyors az internetkapcsolat... = besides the fact that the internet connection is fast...

Without hogy, you would normally need a noun phrase:

• Az internetkapcsolat gyorsaságán kívül... = besides the speed of the internet connection...

That is grammatically possible, but it is not the same structure and not quite the same nuance.

Yes. It is a loanword, adapted to Hungarian spelling.

Hungarian often uses international technical words, but they are adjusted to Hungarian pronunciation and orthography. So szkenner corresponds to English scanner.

That is why it starts with sz, which in Hungarian represents the English s sound.