Ég get ekki komið í dag, en ég kem allavega á morgun.

After some modal/ability verbs in Icelandic (especially geta can / be able to), the following verb often appears as a past participle in neuter singular (sometimes called a supine or sagnbót form), not the infinitive.
So koma (to come) → past participle komið, giving Ég get ekki komið = I can’t come / I can’t make it.
You’ll see the same pattern in very common phrases like Ég get ekki gert þetta (I can’t do this), where gert is also a participle.

get is the 1st person singular present of geta (to be able to / can):

• ég get (I can)
• þú getur (you can)
• hann/hún/það getur (he/she/it can)
  So Ég get ekki... literally starts as I can not...

In a neutral main-clause word order, Icelandic places the negation ekki after the finite verb (the verb that is conjugated for person/tense):
Ég get ekki komið...
The same idea applies broadly: Ég veit ekki (I don’t know), Hún kemur ekki (She isn’t coming), etc.

No. It’s optional. Both are common:

• Ég get ekki komið í dag, en ég kem allavega á morgun. (a bit more explicit/clear)
• Ég get ekki komið í dag, en kem allavega á morgun. (more streamlined)

Repeating ég can sound slightly more deliberate, like you’re clearly starting a new clause.

Time expressions in Icelandic use different prepositions by convention:

• í dag = today
• á morgun = tomorrow

You’ll also commonly see:

• í gær (yesterday)
• í kvöld (tonight)
• á mánudaginn (on Monday)

These are mostly idiomatic pairings you learn as chunks.

Usually not:

• á morgun = tomorrow (general “at some point tomorrow”)
• í morgun = tomorrow morning (literally “in the morning”)

So your sentence uses the general tomorrow meaning.

allavega means something like anyway / at least (in any case). It softens the contrast: not today, but at least tomorrow.
It’s fairly flexible in placement. For example:

• ...en ég kem allavega á morgun.
• ...en ég kem á morgun allavega. (possible, slightly different emphasis)
• ...en ég kem allavega. (if tomorrow is understood)

Icelandic normally uses a comma to separate two main clauses when they’re linked by a coordinating conjunction like en (but):
Ég get ekki komið í dag, en ég kem...

It’s similar to English “..., but ...” when both sides are full clauses.

en is a general but for contrasts:
Ég get ekki komið í dag, en... = I can’t come today, but...

heldur is common in a specific pattern with not ... but rather ..., often after a negation:
Ég kem ekki í dag heldur á morgun. = I’m not coming today but rather tomorrow.
Your sentence is more like a normal contrast, so en fits well.

A few learner pain points:

• Ég: the final g is very soft (often like a voiced “gh” sound), and the vowel is like “yeh” + that soft ending.
• ekki: the kk is a strong voiceless sound; many speakers have a “hk”-like feel in careful speech.
• komið: the ð at the end is often very soft; in some contexts it’s barely pronounced.
• allavega: stress is on the first syllable AL-, and ll is a long “l” sound.

(Exact pronunciation varies a bit by region and speaking speed.)

Sometimes, but it changes the meaning:

• Ég get ekki komið = I can’t come (ability/practical possibility)
• Ég má ekki koma = I’m not allowed to come (permission/prohibition)

So geta is right if the issue is practical (busy, sick, no transport, etc.).

It’s neutral and very natural—fine in both everyday conversation and polite contexts.
If you want it even more casual, you might also hear variants like:

• Ég kemst ekki í dag, en kem á morgun. (I can’t make it today, but I’ll come tomorrow.)
  (kemst emphasizes “can’t manage / can’t make it,” often due to circumstances.)