While I can't answer all of your budgie questions - you'll have to wait for the experts on why your female flaps her wings (I've seen it but it's been a while and either I can't recall or just don't know the specifics for why). Male budgies tend to be very social and flirtatious - this is why if you want to teach a budgie to talk many sources will recommend getting a male (and no other budgie) - although females can learn to mimic human speech as well, generally speaking they are less inclined to do so.
Budgies are very social - so when one budgie starts preening it is common for others to do so as well. This also goes for eating - like many birds they are social eaters. In fact, my own budgies will often eat when I'm eating something in view of them. I hope this answers some of your questions.
Budgies are wonderful. I hope that as you get to know your budgies more that you will be able to build great memories together as you bond.
Last edited by Drummer; 01-18-2018 at 02:35 PM.