Do you get MR nights when using points? Apologies for the amateur question, so here is a slightly harder one: I used points recently to book 2 rooms for 2 nights, both rooms in my name. I got 2 MR nights for the stay. Should I have received 4?

Yes.

Nope. Just 2. You only receive nights credit for the room you stay in.

Just an add-on to this answer. If the OP had paid cash for the 2 rooms, they would have still only received night credits for one room, but you can receive points on up to 3 rooms per night.

Note I do know the OP, in this situation, stated they were using points, but thought this extra info might be helpful for those who might be in a similar situation but were paying cash for their nights.

And one more addition point (based on experience), I've found that I actually tend to get multiple night credits 'per night' at non-FS hotels more than I don't. I don't know why, but I've always guessed either the front desk folks aren't trained on dealing with multi-room reservations as well as at FS hotels or possibly the system software used at non-FS hotels is different than at FS hotels (causing them to accidentally give you to get night credits on more than 1 room per night.)