Learn Hardcore Swedish: Kan du väcka mig tidigt imorgon?

Swedish yes/no questions put the finite verb first. So the modal verb kan comes before the subject: Kan du …?
Du kan väcka mig tidigt imorgon. is a statement, not a question.

Why isn’t there att after kan?

Modal verbs in Swedish (kan, ska, vill, måste, bör, får) take a bare infinitive. So it’s kan väcka, not kan att väcka.

What’s the difference between väcka and vakna?

väcka = to wake someone (transitive). Example: Du väcker mig.
vakna = to wake up (intransitive). Example: Jag vaknar.
In your sentence you need väcka because someone else is doing the waking.

Do I need to say upp, like “wake me up”?

No. Swedish normally uses väcka on its own: väcka någon.
Väcka upp exists but is less common and can sound literary or figurative. Stick with väcka.

Why is it mig and not jag? And what about mej?

jag is the subject form (I). mig is the object form (me). You’re the object here, so mig.
mig is usually pronounced like mej, and mej is common in informal writing. mig is the standard spelling in formal text.

Is imorgon one word or two? I see both i morgon and imorgon.

Both i morgon and imorgon are accepted in modern Swedish. Two words can look a bit more formal; one word is very common. The same goes for i dag/idag, i kväll/ikväll. Informally you’ll also see imorn/imorrn.

Is tidigt imorgon the best place/order? Could I say i morgon tidigt or use bitti?

Both tidigt i morgon and i morgon tidigt are idiomatic; the first is slightly more common.
If you specifically mean “tomorrow morning (early)”, say i morgon bitti or tidigt i morgon bitti.

Is Kan du … polite enough? How can I make it softer?

Kan du …? is fine and polite in everyday contexts. Softer options:

Skulle du kunna väcka mig tidigt i morgon?
Skulle du kunna vara snäll och väcka mig …?
Add snälla or tack: Snälla, kan du …? / Kan du …, tack?

Where does the negation go? Is Kan du väcka mig inte … okay?

Put inte after the subject when the verb is first: Kan du inte väcka mig tidigt i morgon?
Kan du väcka mig inte … is ungrammatical. Note that Kan du inte …? can be a genuine negative question or a polite nudge depending on tone.

Why is it tidigt and not tidig?

Tidig is an adjective (early) used with nouns: en tidig morgon.
Tidigt is the adverb (early) used with verbs/adjectives: väcka mig tidigt.

Can I drop the subject du?

No. Swedish normally requires an explicit subject, so you need du.
The only natural subjectless option here is the imperative: Väck mig tidigt i morgon.

How would I say this as a command/request using the imperative?

Use the imperative väck: Väck mig tidigt i morgon.
To soften it: Väck mig tidigt i morgon, tack. or Snälla, väck mig tidigt i morgon.

Is there a formal “you” I should use instead of du?

Modern Swedish generally uses du, even with strangers. Ni can appear in service contexts, but overuse may sound old-fashioned or stiff. Kan du …? is standard.

How do you pronounce the tricky words here?

väcka: roughly “VEH-kah”; short ä (like e in “bed”), and double consonant gives a short vowel.
imorgon/i morgon: roughly “ee-MORR-gon”.
mig: usually pronounced “mey” (spelled mej informally).

How is väcka conjugated?

Infinitive: väcka
Present: väcker
Past: väckte
Supine (used with har/hade): väckt
Imperative: väck
The short vowel ä is indicated by the double consonant ck.