I went back and forth on this issue for a while. On one hand, I love the browser version on the iPad. I love that it is the actual site, instead of a dumbed down version of it. I do not really like Facebook chat, because it tends to get annoying.
At the same time, I do miss the notifications when I get posts and messages. I even went back into the facebook settings, and turned email notifications back on, but i quickly remembered why i turned them off in the first place. I hate my inbox filling up with all of the Facebook nonsense. I turned them back off and was hoping for a Facebook iPad app, but then I thought about it. I get those same notifications on my iPhone 4, and it really isn't really necessary to get the notifications in more than one place.
For now, I will stick with the browser version, and if facebook releases a larger version of their iPhone version, I will most likely stick with the browser. However, if they release a more functional iPad friendly version, then we will have to wait and see.
1) I'm not permanently logged in. The session keeps me in for awhile, but I inevitably have to re-log in a few times over the course of the day. It's not a big deal, but it is annoying.
Log in, and go to your facebook home screen. When you are there, click the Plus sign at the top bar of the safari browser. Then click add to home screen. It should then be an icon on your home screen, and if you use that to go to the site, then it should keep you logged in.