my gmail is my account with facebook....I do get email notifications instantly, obviously actual FB notifications is MUCH more preferable.
I use Ebuddy for online chat, FREE APP and works perfect, it combines all my IM accounts just like trillian does on the computer, in fact Ebuddy does the FB chat way better then trillian.
so at least you can get your FB chat on with ebuddy!
the FB app is terrible overall, BBerry's was terrible too but at least you got notifications that sync'd with the actual app.