Hee, hee. I haven`t done this sort of thing for three decades. Let's see what I remember.
1. I agree. Also called copula verb, or is this Spanglish?
2. IMO 'to study' is an infinitive always.
3. I disagree. The subject complement isn't necessarily always an adjective. It can also be a noun or noun phrase. Cf. 'Hedwig was my grandmother'. I'd say 'to study' works as a noun here. A nominal infinitive or some such name?
= Not a teacher. Used to be a student. =