1. b. you use queria because if you say "quise" it means you stopped wanting to learn ballet sometime in the past.
2. b. you use conoci' because you've already met the professor in the past
Answer:
The question is asking if your going to see your friends over the weekend.
So what you can write is
Si, yo voy a ver a mis amigos esta semana. ( Yes, I'm goin gto visit my friends this weekend.)
or
No, yo no voy a ver a mis amigos esta semana. ( No, I;m not going to visit my friends this weekend.)
Hope this helps:)!!!