Manuel told Buck that they were going out for a walk. Seeing that Buck trusted the people at the mansion, including Manuel, Buck went with him. It wasn't until they got further away from the mansion did Manuel put a rope on Buck. Hope this helps! :D
It's not something you hear - it's "The buck stops here." Both sayings refer to passing on responsibility. If you "pass the buck," you refuse to accept responsibility for whatever's going on, and if it stops here, you do accept it.
Manuel sold Buck to some random guy in a park while trying to get some money for his gambling. After that Buck was passed on and on to the Man in the Red Sweater. This man harassed Buck with a club trying to break him in.
Once the doe and buck have mated you should separate them. ESPECIALLY when the babies are born. The buck can trample the babies when there still hairless or when they're older the buck will try to mate with the does of the litter.