The schools in Lehi are in alpine school district, which is a good district, but there is a lot of overcrowding. When you move here you'll see why. Tons of young families and tons of kids! I don't know what you can do about the big classrooms, other than looking into charter school or private school. My kids' class sizes are bigger than I'd like, too, but they're doing okay.
As for piano and dance, ask your neighbors when you get there. Chances are there will be someone in your neighborhood who teaches piano lessons, or your neighbors will be able to recommend whoever their children take from. You will probably find home dance studios as well; there are three within a 5-minute drive of my house, and I imagine Lehi is similar.
I don't remember seeing any episcopalian churches in the area, but I did find this website from the anglican diocese of Utah that might help you find something:
The Episcopal Diocese of Utah Welcomes You!
Good luck!