Yea, they are correct, good job! However, in my opinion, they seem a bit incomplete without context. I think the subject of these sentences is "I".
2. 私は8時半に学校に帰ります or 戻ります。(I'll go back to the scholl at 8:30.)
(*I go to the school at 8:30. = 私は8時半に学校に行きます。)
3. 私は日曜日に喫茶店に来ます。(It means you are in the cafeteria now.)
(*I go to the cafeteria on Sunday. = 私は日曜日に喫茶店に行きます。)
Also, I know 家 is usually used for いえ, but is it also commonly used for うち?
--> Yes, in normal convesations, うち is used more than いえ, it is more like HOME.
I hope this was helpful.