It is my understanding that Watchcare Programs are not used much anymore, although you say many churches have it. Generally, people just move their membership back and forth. Or they attend a local church without ever officially joining the church.
(Trotter, Watchcare is/was a program where a person could "join" a local church under "Watchcare" but still remain a member of their home church. For instance, a missionary or a college student who attended a local church but was receiving financial support from their home church. The local church would "watch over" them while they were away from their home church.)
As for #2, I don't know of any Baptist church that would let a non-Baptist (or any non-member, for that matter) serve as a SS teacher or any other position in the church. In my church, you must be a church member (thus, a Baptist) to serve in most areas. (We have a lawncare team and some of the people who serve on it are not church members, but just enjoy it and want to help. They usually are friends of church members. But that's the only area I can think of off the top of my head that one does not have to be a church member in order to serve.)
However, I don't "get out" much, so I could be mistaken as to what other churches do!!