Learn Hardcore Icelandic: Það er erfitt að vakna mjög snemma.

Yes. In Það er erfitt að …, það is an expletive (dummy) subject that doesn’t refer to anything; it helps satisfy Icelandic main-clause word order (the finite verb er appears in second position). You can also say:

Að vakna mjög snemma er erfitt. (the infinitive clause acts as the subject)
Erfitt er að vakna mjög snemma. (more formal/emphatic)

Why is erfitt in that neuter -tt form?

Predicate adjectives agree with the grammatical subject. With dummy það, Icelandic uses neuter singular by default, hence erfitt. With real subjects you see normal agreement:

Dagurinn er erfiður. (masc.)
Vikan er erfið. (fem.)
Verkið er erfitt. (neut.)

What is að here? Do I always need it?

Here að is the infinitive marker, equivalent to English to. You normally need it before an infinitive in this kind of complement clause: … erfitt að vakna …. Many modal/auxiliary verbs take a bare infinitive without að (e.g., vilja, mega, geta, skulu, munu): Ég get vaknað snemma. Others still require að (e.g., þarf að, reyni að). Note this að is different from the preposition að (to/towards, governs dative) and from að meaning that introducing a clause.

Why is it vakna and not vakna upp? And what about vekja?

vakna = wake (up) by yourself; intransitive. This is what you want here.
vakna upp exists but is either colloquial/pleonastic or used in the set phrase vakna upp við [e-ð] = wake up because of vaknaði upp við hávaða.
vekja = wake someone/something (transitive): Ég vek þig kl. 7.

Is mjög snemma idiomatic? Could I say mjög erfitt instead?

Both are fine, with different focus:

mjög snemma emphasizes the earliness: It’s hard to wake up very early.
mjög erfitt emphasizes the difficulty: It’s very hard to wake up early. You can combine them (Það er mjög erfitt að vakna mjög snemma), but that can sound a bit heavy.

Can I move the adverb phrase around?

Inside the infinitive clause, the natural spot is after the verb: að vakna mjög snemma. You can front it for emphasis in the main clause, but keep verb‑second order: Mjög snemma er erfitt að vakna. Another common variant is to front the whole infinitive clause: Að vakna mjög snemma er erfitt.

How do I say it’s hard for me to wake up early?

Three idiomatic ways:

Það er erfitt fyrir mig að vakna snemma.
Ég á erfitt með að vakna snemma. (very natural: I have difficulty with…)
Mér finnst erfitt að vakna snemma. (I find it hard…)

Is snemma the only way to say early? What about fyrr/fyrst or árla?

snemma = early (general adverb); your sentence is idiomatic.
fyrr = earlier (comparative), used with comparisons: Ég vakna fyrr en áður.
fyrst = first/firstly; not used to mean early in this sense.
árla = early, somewhat formal/literary, often in árla morguns (early in the morning).

What overall grammar pattern is this?

It’s an impersonal predicate with an infinitival complement: Það er [adjective] að [verb]. Very productive, e.g.:

Það er gaman að læra íslensku.
Það er erfitt að keyra í snjó.
Það er ómögulegt að svara strax.

Can I drop það?

Not in this word order. You can either:

Promote the infinitive clause: Að vakna mjög snemma er erfitt.
Use a marked order: Erfitt er að vakna mjög snemma. Simply deleting það from Það er erfitt … is ungrammatical in a main clause because Icelandic wants something before the finite verb.

Any quick pronunciation tips?

þ (in það) = voiceless th as in English thin.
ð (in það) = voiced th as in this; in fast það er, the ð often disappears, so it can sound like þar.
j (in mjög) = English y.
ö (in mjög) = rounded vowel like British bird, but rounded; the final g is a soft fricative, not a hard g.
Double consonants (erfitt, snemma) make the preceding vowel short; r is tapped/trilled.

Why isn’t there any object or reflexive?

Because vakna is intransitive and inherently means to wake up oneself. You don’t use sig with it. If someone wakes someone else, use vekja with an object.

Could I use til að here?

Not for this meaning. til að + infinitive expresses purpose: Ég set vekjaraklukkuna til að vakna snemma. In your sentence, að vakna is a complement to erfitt, so plain að is correct.

How do I say too early?

Use of (too): að vakna of snemma = to wake up too early. For emphasis: allt of snemma = way too early.