sophomore in a sorority

Most likely yes you can join, but it is unlikely you can move in right away. Most houses either won't have space, or if they do they will want to interview live-ins before you move in, and if the interview goes south you may not be accepted. But if you're ok with living out, it'll be more likely you'll get accepted because most sororities nationally want girls to be able to keep their alumni status, which only works if they can graduate with their letters

It depends on the house. In mine we had a girl transfer in from the east coast over the summer and she moved in and its been great. I know she had to meet with the president and some other people but it was very casual, as long as you get along with everyone it should be fine.

The only issue in joining would honestly be if the chapter youre trying to join is really exclusive here (theta/pi phi) and not like that at your school, but if youre transferring anywhere in the middle it should be fine. Good luck! and email the president of the UW chapter of your sorority now so you can find out!