1. The login on touch.facebook.com is pretty much broken for everybody at least some of the time. Yeah, it sucks. What you do is, click Full Site or something down at the bottom, log in on the "real" Facebook, and then browse back to the lite version of Facebook Mobile.
2. The full version of the mobile site is a bit trickier to find. I'm sure there's an easier way, but I rarely see it. It's basically what the mobile site should be, but I think the lite mobile site (the one you probably see the most at touch.facebook.com) is easier for newbies.
3. The Facebook app sucks until you update it. Just look for Facebook For Android by Facebook on the Market. It'll act like a new app until you install it -- and it'll port all your settings to the new version.
4. But even better than Facebook in the browser and the app is TweetDeck, especially if you also have a Twitter. And it manages multiple accounts as well (at least for Twitter).