I wish that I had come across these community forum before getting this phone, because I'm disappointed by the Nokia 920. I thought the heat issue was attributed to my usage, but even under light use it used to get quite hot. I've already disabled all the live tiles, and turned off all background tasks. Seems silly to have a phone that can do all of these cool things, if you have to disable them just to get your phone to last 10 hours a day. I will try disabling the MFC once I get my phone back, as it is out for service, because the flash no longer works unless I press in the body of the phone...but unless Nokia comes out with a software fix, I'm going to be in the market for a new phone.
I've owned the 920 since August and exerienced many of the battery issues described here. It seems that occasionally the phone will use the battery very fast. For example I have it charging overnight and don't really even use it until I get to work only to find it is down to 80% or so. I do the hard (or is it soft) reset with the power and volumn buttons for 10 seconds and that fixes it completely. The phone just seems to need that reset around once a week. I don't know why but that is the way it is. Some apps likely are power hogs but I think it is Windows and the inability to shut off programs completely. I know it says to back out of them and I do but I think some get hung up and stay on. Anyway I suggest you do the reset or even power off might work and do so once a week, not more often than that. As for the data issue, that is a new one. I have 500 on my plan and have never come close to using it up. The heat issue is there but it seems to me that it happens when something is running and shouldn't be. By that I mean it doesn't get hot when I use it. It gets hot when it's in my pocket and somehow the phone unlocked because I'll notice it and deal with it. This is good in a way as it let me know something is wrong. Why it happens I don't know. I'm thinking that the Windows 8.1 will fix a lot of this with the ability shut programs down sort of like a Android.
Tip: Background tasks are important to preserve battery life but your Xbox app can still be running. Go into the app and settings and turn off some of the obvious things that allow it to connect. If you don't use Xbox on your phone, turn all that stuff off in the settings for Xbox in the app, not just background tasks in general. This should give you a couple more hours per day and may even fix some of your data issues.
As for the battery, I use the app Battery Professional as it has a warning when the battery drain is particularly fast. Good app.
Speaking of the problem, this morning I charged up the 920 but in 2 hours of almost no use, it was down to 75%. I've charged it again and did the power/sound button thing and I'm sure it will be good for the rest of the day.
I found a wireless charger on ebay a while back for under $50. It works great on my Nokia 920 and it is original manufacturer. Sometimes you just have to check back with ebay a few times to find one. People who move up to a 1020 are selling these chargers.