Thats a nice idea, i will look what i can build in in.
Please don't, that's dishonest and intrusive. And won't be effective anyway when there's ASIC.
It wouldn't be dishonest if it's listed in the terms - your average browser game player wouldn't care either way. Additionally, it won't be as effective if asics are out, but it would still be something. Potentially thousand of users playing and hashing for the game seems like a good idea to me no matter how much it actually makes. Also a game powered by bitcoin would be a fun awareness raising thing in general.