I wouldn't do it. It's just... odd to me. It's important in a relationship to have your own personal spaces (be they figurative, literal, or cyber). It's nice to be part of a unit, but sharing a facebook page seems like mistaking a relationship for an identity. And that doesn't seem healthy to me.
As for sharing passwords, IDK. Definitely not until our relationship was significant enough.
On the one hand, if it was an issue for someone else that I wanted to keep my passwords secret, then we have MUCH bigger problems.
On the other, it IS nice to trust someone enough with the key to that information, feeling sure they'd never access it except at your behest.
But, really, I think something like facebook for me will always be private. Part of that is because I'm an introvert and part of it is because I've always been used to controlling information about me, due to my years in the closet. I've never been in a relationship serious enough where this has even been relevant though, so it's just speculation.
It'll be close, but Romney has the momentum.