I really think you should consider returning the phone for a replacement, you're having issues that are far from common and a high level of instability, assuming you're running a stock rom it's almost definitely a faulty unit...
It's starting to look that way. I've not rooted or anything but I have been using widget locker, replacement launcher and replacement message app. I've taken all taken all that off and will wait and see if it is any better. I really don't want to go through the hassle of a replacement set unless i'm sure it's the hardware!