Hún er betri á gítar en ég.

A natural breakdown is:

• Hún = she
• er = is
• betri = better
• á gítar = at guitar / on guitar, meaning at playing the guitar
• en ég = than I (am)

So the whole sentence means She is better at guitar than I am.

Betri is the comparative form of góður, which means good.

This is an irregular pattern:

• góður = good
• betri = better
• bestur = best

So Hún er betri ... literally means She is better ...

This is a very common question.

• betri is an adjective: better
• betur is an adverb: better / more well

In this sentence, Icelandic is describing her: She is better at guitar. Because it describes the person, Icelandic uses the adjective betri.

Compare:

• Hún er betri á gítar en ég. = She is better at guitar than I am.
• Hún spilar betur á gítar en ég. = She plays guitar better than I do.

The first compares people; the second compares how they play.

Yes. Since betri is an adjective linked to the subject through er (is), it agrees with the subject in the usual Icelandic way.

In this sentence, the subject is hún (she), so the adjective is in the form used for that kind of subject.

Even if you do not yet know all the adjective endings, the important point is:

• betri here is not random
• it is the correct comparative adjective form used with hún er ...

With musical instruments, Icelandic very often uses á in expressions about playing skill.

So:

• spila á gítar = play the guitar
• vera góður á gítar = be good at guitar
• vera betri á gítar = be better at guitar

This is idiomatic. You should learn á gítar as a set expression meaning on guitar / at playing guitar.

Because Icelandic often leaves the instrument generic in this kind of expression.

So á gítar means something like:

• on guitar
• at guitar
• at playing guitar

It is about the skill in general, not one specific guitar.

If you added the definite article, it would more strongly suggest a specific instrument, not just the general ability.

Because en here is understood as introducing an omitted clause:

• Hún er betri á gítar en ég er.
• She is better at guitar than I am.

Since the full idea is than I am, Icelandic uses ég.

So en ég is like formal English than I, not than me.

Yes. That is completely fine.

• Hún er betri á gítar en ég.
• Hún er betri á gítar en ég er.

The shorter version simply leaves out the second er because it is understood.

This kind of omission is very common and natural.

Both are natural, but they focus on slightly different things.

• Hún er betri á gítar en ég.
  = She is better at guitar than I am.
  This talks about overall ability or skill.

• Hún spilar betur á gítar en ég.
  = She plays guitar better than I do.
  This focuses more directly on the action of playing.

In everyday use, the difference is often small, but the grammar changes:

• betri = adjective
• betur = adverb

A rough English-style approximation is:

hoon er BEH-tri ow GEE-tar en yeg

A few helpful notes:

• ú in Hún is like oo
• á is like ow
• gítar has stress on the first syllable: GÍ-tar
• ég begins with a y sound, roughly yeg

This is only an approximation, but it is a good starting point.