If I have blocked someone on Twitter, but they follow people I follow and people that follow me, if our shared followers retweet one of my tweets, do they see that? Also, if a shared follower mentions me in a tweet, will my name appear in that tweet?
Question 1: If our shared followers re-tweet one of my tweets, do they see that?
No, your tweets are not appeared the blocked person's timeline. However the tweets are visible to the blocked person by viewing the shared person's timeline.
Question 2: If a shared follower mentions me in a tweet, will my name appear in that tweet?
Yes, if the shared person mentioned your name in his/her tweet, your name will appear in the blocked person's time line.