A sávszélesség nagy, és a letöltési sebesség gyors.

Because Hungarian usually omits the verb for to be in the present tense, third person singular when the predicate is a noun or an adjective.

So:

• A sávszélesség nagy = The bandwidth is large
• A letöltési sebesség gyors = The download speed is fast

The missing verb would be van, but here Hungarian normally leaves it out.

A is the Hungarian definite article, meaning the.

Hungarian has two forms:

• a before a consonant
• az before a vowel

So:

• a sávszélesség
• a letöltési sebesség

Both nouns begin with consonant sounds, so a is correct.

Because the sentence contains two separate noun phrases / two separate clauses, and each definite noun phrase needs its own article.

So Hungarian says:

• A sávszélesség nagy, és a letöltési sebesség gyors.

Not:

• A sávszélesség nagy, és letöltési sebesség gyors.

The second part needs its own subject phrase: a letöltési sebesség.

It is a compound noun:

• sáv = band, strip, channel
• szélesség = width

Together, sávszélesség means bandwidth.

This is very normal in Hungarian, which often forms long compound words where English might use a shorter technical term.

Because letöltési is an adjectival form.

Here is the basic idea:

• letöltés = download / downloading
• letöltési = related to downloading, download-

So:

• letöltési sebesség = download speed

The ending -i often turns a noun into an adjective meaning related to or belonging to.

Similar pattern:

• iskola = school
• iskolai = school-related, school-

So letöltési sebesség is the natural Hungarian way to say download speed.

Because Hungarian uses different natural adjective pairings with different nouns.

• nagy sávszélesség = large/high bandwidth
• gyors sebesség or more naturally in context gyors a sebesség = fast speed

Even if English might say high bandwidth and fast download speed, Hungarian chooses adjectives according to what sounds natural with that noun.

So:

• nagy = big, large
• gyors = fast

This is mostly a matter of normal usage and collocation.

Because here nagy and gyors are not directly describing the nouns inside the noun phrase. They are the predicate of the sentence.

Compare:

• a nagy sávszélesség = the large bandwidth
  
  • adjective inside the noun phrase
• A sávszélesség nagy. = The bandwidth is large.
  
  • adjective as the predicate

And:

• a gyors letöltési sebesség = the fast download speed
• A letöltési sebesség gyors. = The download speed is fast.

So adjective position changes depending on the structure.

Yes, you could also say Nagy a sávszélesség.

Both are grammatical, but they have a slightly different feel:

• A sávszélesség nagy.
  Neutral, straightforward statement.

• Nagy a sávszélesség.
  More emphasis on large.

Hungarian word order is often influenced by topic and focus, so changing the order can shift emphasis even when the basic meaning stays the same.

Because és is joining two clauses here:

• A sávszélesség nagy
• a letöltési sebesség gyors

Even though the verb van is omitted, both parts still function as clauses, so the comma is normal.

Compare this with a case where there is just one clause with two adjectives:

• A sávszélesség nagy és stabil.

There, no comma is needed before és.

A few useful pronunciation points:

• s = English sh
• sz = English s
• gy = a soft sound somewhat like dy, but not exactly
• á = a long a
• é = a long ay
• ö = a rounded vowel, similar to German ö

So:

• sávszélesség
  starts with sh, not English s
• sebesség
  starts with sh too
• gyors
  begins with the special gy sound

Also, Hungarian stress is usually on the first syllable:

• SÁVszélesség
• LEtöltési
• SEbesség
• GYORS

No. Hungarian has no grammatical gender, and adjectives do not change the way they do in many Indo-European languages.

So:

• nagy stays nagy
• gyors stays gyors

They do not change for masculine/feminine/neuter, because Hungarian does not have that system.

That is one reason Hungarian adjective use can feel simpler than in many European languages.