Bardium, I've had the cannot delete email problem and it is just a setting that needs changing. Perhaps something that got lost in restore. I can't quite recall exactly which one but I just googled it and the answer is somewhere here on this forum..
Regarding the crashes....I had the same problem and after Apple guiding me to do the restore as you have done, the problem remained. So much so that I couldn't go into iTunes at all.
It's now on the way to apple for repair or replacement. Apple support told me it is a memory fault.
What concerns me is, a potential replacement takes over the warranty period of the original as explained to me yesterday by Apple. As this is a progressive problem, then hypothetically, the replacement going wrong after the same period would be at the end of the warranty period. If I'm dissatisfied with a repair or replacement, do I have the right to a refund?