이불 would be better translated as comforter I guess. It's a big, thick blanket in any case. 담요 is like a blanket you'd use on a couch or something
Ah, the invisible ㄴ. My least favorite phonological rule in Korean (especially since it is inconsistent in the expected phonological environment, rendering it impossible to describe succinctly). I hope people notice your post, thank you! The robot has it right but it's easy to miss for repeating the correct way.
I don't see why there is "please" in the sentence. It would have been perfectly fine if it was just "Give me a blanket." If you really wanted to use "please", just add 제발 in front of the sentence and than "please" would actually be more fitting to the translation.