I'm not sure about the LOA, because I haven't done it. I would think that with nearly a year under your belt, though, you ought to be senior enough to at least get a couple of days off that you need. I don't know about three weeks for a honeymoon or whatever, though. Might be worth asking at your interview.
PBS basically just sorts out what everybody wants. They load in all the trips, crewmembers put their preferences in, and then it executes and tries to give everybody as much of what they want as possible, while attempting to respect seniority. It's not perfect, and a lot of people complain about it, but I'd say I like it overall. It has quite a few options, but it your case, for example, you could ask it for commutable 4-day trips with 4 days off between trips, or whatever you like. You won't necessarily get it, but the system will try.