When I use TOR, is there any way that the family could see I use it?
Assuming a family member is technically savvy enough, yes, they could probably tell you are using TOR. The easiest way to do this would be to sniff the outbound packets on the network and analyze them using the TOR dissector in Wireshark. TOR packets are easily identified, as are TOR entry nodes.
Yes, in almost all cases. In general WPA use PSK, which means anyone with the password case decrypt and sniff packets. If this is a concern there is one exception, and that is WPA-Enterprise. From http://www.ciscopress.com/articles/article.asp?p=1576225
Users never deal with the actual encryption keys. They are securely created and assigned per user session in the background after a user presents their login credentials. This prevents people from recovering the network key from computers.
So this means that each computer uses a unique key for their wireless encryption so another computer with access cannot sniff someone else's wireless connection.