Well it seems to be solved. I just found out after not having received mms for a long time.
After last OS-update the mms settings was cleared. I typed in my providers settings and started to receive mms again. The battery does not drain anymore ?????
When these settings are missing, does the phone do a lot of communication on the network ???
After trying many different things, I was able to find a work around for this issue.
The issue that I had seemed to be from the Exchange accounts that I had associated with my phone. I turned push notification off and Fetch to manual. On the advanced menu, I did the same for all accounts, manual. This is keeping the phone frmo trying to check email until I want it to. If Mail is not active, it does not try to check email.
I was able to finally find the root cause of at least one of the battery drain problems, and it has nothing to do with email push notifications. I believe this issue may even be in iOS 7 as well. When calendar entries are added to the calendar from an inbound email, sometimes the Notification Center (main screen pulldown) will jitter the entry. That is, you'll see it added and removed very quickly from the notifications list. This error seems to take a page from Apple's business address (1 Infinite Loop) because that's exactly what appears to be happening here in the Notification Center. As long as the calendar entry continues to jitter indefinitely in the Notification Center, the CPU load will remain high and the battery will drain rapidly.
The way to stop this requires clearing all notifications related to calendar from the Notifications pulldown and turn Calendar off from showing in the Notification Center through Settings. Note, even though it is a pulldown, the notification area remains active out of sight. So, the CPU is still consumed managing these entries even if you don't see it or check it. Note that other jitter may also be happening in the Notification Center from other apps. So you'll want to remove these from the Notification Center if you also find them to be a problem. To avoid these random drain issues, it might be wise not to have anything in the Notifications Center except those things you absolutely need there.