I would definitely assume he can tell Anna's not human, whether or not it'd be specific enough to tell she was an angel is probably more a question for your end than mine, but let the record show that I'm fine with it! Also her emotions will be rather enhanced lately anyway too, it'd be like a bright red flag waving in your face so I'd be surprised if he couldn't at least sense that. She's a bummer right now angelic prison is a bitch.

In terms of the second half, maybe? It's a bit more grey area, obviously it'd be harder than with a normal mind, but on the flip side she's a lot more humanized than most Angels so perhaps minorly? Case-by-case circumstance, shall we say :)