I blocked someone on Twitter, but then I favorited one of their tweets when I went through their page. Will they be able to see that I liked their tweet?
Yes, they do.
Blocking simply removes someone from your follower list and prevent them from contacting you (via their usual account, they can use another one of course) by direct message or @ mention - however they can still post @ mentions and others can view them (and you can see them if you search for them).
The person can see you have favorited their tweet. The only thing is you don't get a notification if they favorite your tweet (because you blocked them they didn't block you).
No, they cant. Or else it would defeat the whole purpose of the "block" concept. Go ahead without hesitation.