yes, it's a reflexive pronoun. "se" is accusative case, there is also "si", which is dative case (both would be "sich" in German).
That's an old, useless grammar rule. Nobody speaks or writes like that. A quote from Winston Churchill, "That's the sort of pedantry up with which I will not put." Hanging prepositions are a very common thing in English, no longer considered bad grammar
I guess I did not get that memo. I agree with Clive and generally that grammatically correct answers at least be accepted.
If you go around saying "At what are you looking?" people will stare at you like you have a disease.