Like the others said, gthe BHA will be for her duty location, BCT and AIT. Doesn't matter where her dependents are... my dependent was in Germany, and they said, hell no, you will not get that!!!.
She doesn't have to be a citizen, as long as her MOS doesn't require a clearence. As long as she has a GC she is good, beside, now days, they get the citizenship while in AIT, if she puts the papers as soon as she gets to AIT.
I don't think she she needs a waiver for dependents. Only single parents need that...she has you, so you are her family care plan.
Just some information for you...she will have a slight chance to be station in Philipines, so if you decide that you will not move from there, she will always get BHA for the place she will be, and no FSA. Unless she will be station overseas on unaccompanied tour...and even then, it has to be approved to let her family to move to Philipines, so...something to think about.
Oh, and yes, she will most likely come in as Specialis, since she has a BA... it just had to be recognized in US, if she has it from a school outside of US.