2.) I don't know if it's because I use Dolphin Browser, but I have tab browsing as well as he ability to see my notifications bar/e-mail updates. All i have to do is pull down the notification bar and click and it brings me right ot my e-mail.
8.) My gmail works fine. I get a little @ notification, click on it, and it shows me the e-mail.
There is an OTA Fix (Over the Air) set to come out December 11th and then in January. Hopefully all the bugs that have been coming up will get cleaned up. There are just certain things that even beta testing doesn't reveal. This is true with any new phone, you generally wait for the first update. (Especially with something like an iPhone)