Learn Hardcore Filipino: Lumabas ako sandali.

Yes. Lumabas is actor-focus in the completed (perfective) aspect, which usually maps to simple past or present perfect in English. So Lumabas ako sandali can mean “I went out briefly” or “I’ve just stepped out for a moment,” depending on context or added time words.

What’s the root of lumabas, and what does the -um- infix do?

The root is labas (“outside; to go out”). Inserting -um- after the first consonant makes an actor-focus verb. Aspect forms:

Completed: lumabas (went out)
Imperfective/ongoing: lumalabas (is/was going out; goes out habitually)
Contemplated/future: lalabas (will go out)

Why is it Lumabas ako and not Ako lumabas?

Tagalog is typically predicate-initial: the predicate (here, the verb) comes before the subject. So Lumabas (predicate) precedes ako (subject). You can front the subject for emphasis or formality:

Ako ang lumabas sandali. (It was I who went out briefly.)
Ako’y lumabas sandali. (Formal/literary.)

What does sandali mean? Is it the same as saglit?

Both mean “a moment/briefly” and are interchangeable in most contexts. As an interjection, means “Just a moment!”