Perplexing sentences

1. I haven't met Tom.......the last week.

a) since b) for

My answer :

I think both 'since' and 'for' are OK. Am I right?

2. Have you done your homework....? - You are quick!

a) yet b) already

My answer:

I go for 'already'. Is using 'already' in interrogative different from using it in statements?