Went through this exact problem. I was using google's ecosystem for both contacts and e-mail.
Google contacts, imported into Live.com, wouldn't show, I tried everything, including a new Live account from scratch.
Facebook contacts also didn't show by purely importing Facebook contacts into Live.com. Some people have claimed to get it to work but I haven't.
Either way, if you don't want to move off Google, you can bypass syncing these things on the web Live.com portal, and instead do it on your phone. Just add a gmail account on your phone, check the option to sync contacts, email, calendar etc. Do the same with Facebook, on your phone, not on the web portal.
However, I decided to switch over from Google's services to Live's. The integration with Hotmail is unbelievable. Delete email on your computer, it's instantly gone from phone. Delete an email on phone, its instantly gone from computer. Folders sync flawlessly. All in all it's definetely tighter than Google integration on this phone.
I also exported my Google contacts as an outlook file, then imported them into Live.com. All the fields carry over fine, you get an exact replica of your contacts on Live.com. Now I'm just using Live for contacts, e-mail, calendar etc. Google doesn't really bring that much more to the table, and the tighter integration with the phone is worth it to me.
I also now forward all my Gmail messages to my Live inbox. Now I'm just using my Live inbox full time. My gmail will just be archived eventually.