where would Ты go to find out about public appearances of Остаться в живых cast members??

Well right now the cast is pretty busy shooting the 6th season and the rest of the time they're probably busy with personal stuff или other work.

You're best bet is to scope out some big media conventions (comic con's and the like) and see if a cast member is doing a public appearance или a panel on a Показать или movie they're doing.