How do u ask your mum for a フェイスブック so あなた can catch up with all of your old pals and also your boyfriend when he finally askes あなた out?

Well...firstly don't call him your boyfriend as clearly he isn't and that's just weird and almost going to hit stalker status.

Did あなた ask your mum to 登録する Fanpop? if yes, just ask her the same way. If no then do what あなた did to 登録する Fanpop.