I don't understand how anything in this is confusing.
Log on once every 24 hours to basically renew your certificate. If I log in at 3PM Tuesday, I can play games until 3PM Wednesday. IF they kick you off from playing games, that's ****ty. But if they let you play until you quit, and then deny access to your games, it's still ****ty, but it allows you to have offline gaming.
If you want to play your game at a friend's house, log onto your account on their Xbox. Basically, a mobile game library.
"...and any one of your family members can be playing from your shared library at a given time" is the only one that caused any confusion, and I just don't know if you are limited to one family member or how they deal with playing the same game (ie, could I play Halo with my cousin who signed in on my account?).