Facebook is indeed searchable. There is a search bar on the site. We made around 10-15 members in about one/two days.
Regarding battery leakage, this is something which you can try to repair by replacing the battery, cleaning up any acid leakage from the board and then perhaps soldering wires onto the board where the old battery used to be so that the new battery can sit somewhere off the board. Either that or encapsulate the battery in some sort of casing!
Cheers for now