Would "he is writing" be "Scriobhann ag se" or "Ta se ag scriobh"?
The second one, tá with a verbal noun.
Yes, exactly. "Tá se ag scríobh/ ith/ rith = he is writing/ eating/ runing".
Ag ithe, actually.
Could this sentence also mean "It writes?" Let's say we are talking about an automated computer program, or an alien of indeterminate gender.
If the "it" in question is a grammatically masculine noun, sure. If "it" is grammatically feminine, use sí.