Fique aqui até eu voltar.

Fique is a command form of the verb ficar (often “to stay,” “to remain,” “to be/stand somewhere”). In this sentence it’s telling someone to stay here.
Grammatically, fique is the affirmative imperative used with você (and also with o senhor / a senhora).

Because Brazilian Portuguese has different command forms depending on who you’re addressing:

• Fique aqui... = command to você (more neutral/polite)
• Fica aqui... = command to tu (or informal spoken usage in some regions)

In much of Brazil, people use você a lot, so fique is very common as a standard “stay.”

It’s usually neutral to polite, not necessarily stiff-formal. It fits well for:

• speaking to a stranger
• speaking politely to anyone
• giving a clear instruction

More explicitly formal would often include titles, e.g. Fique aqui, senhor.

After até (“until”), Portuguese normally uses:

• infinitive: até eu voltar (“until I come back”)
• or sometimes subjunctive: até que eu volte (“until I come back”)

Using indicative like até eu volto is not the normal pattern here. The sentence is about a future point that hasn’t happened yet, so Portuguese prefers infinitive (very common) or subjunctive (also correct, often with até que).

Yes—this is a very typical Portuguese pattern: infinitive + explicit subject.
In até eu voltar, the verb voltar is in the infinitive, but eu tells you who will do the action. English can’t do this directly, but Portuguese can.

Yes. Fique aqui até voltar is possible and usually understood as “until I come back,” because context makes I obvious.
Including eu (até eu voltar) makes it a bit clearer/emphatic about who is returning.

In your sentence, aqui belongs to the first part (Fique aqui = “stay here”).
If you want to specify that your return is to here, you could add it to the second part, but it can sound redundant:

• Fique aqui até eu voltar. (most natural)
• Fique aqui até eu voltar aqui. (possible, but often unnecessary)

Often yes in meaning, but the feel can differ a bit:

• Fique aqui até eu voltar. = very common, straightforward, conversational
• Fique aqui até que eu volte. = also correct; can sound slightly more “structured” or emphatic

In Brazil, the infinitive version (até eu voltar) is extremely common.

Usually no comma. It’s one continuous instruction: “Stay here until I come back.”
You might add a comma only for a pause or extra emphasis in certain styles, but it’s not standard/necessary.

A rough guide:

• Fique ≈ FEE-kee
• aqui ≈ a-KEE
• até ≈ a-TEH (stress on -té)
• eu ≈ eh-oo / yoh (often like a quick ew sound)
• voltar ≈ vol-TAR (final r often sounds like a soft h in many accents)

And don’t miss the accent: até has é, showing the stress and open vowel.