Sounds like you're seeing a lot of problems. Did you happen to take note of the battery percentage when these things happen? The reason I'm asking is that although you've swapped batteries, it could still be a battery problem. I know it sounds far fetched, but I own 4 spare batteries. One of these batteries will cause random reboots, and it always happens when the battery has about 47% left. My phone doesn't get a random reboot if I use the other 3 batteries no matter what the percentage is. However, as soon as I start using this one battery, the phone runs perfectly until it reaches 47%, and then the phone reboots on it's own. After that first reboot, the phone will reboot again randomly and cause all kinds of issues until I swap out it out. Needless to say, I don't use this battery anymore.
It may not be your battery, but if your phone runs fine for a period of time, and then starts doing some weird stuff, take note of the battery percentage and see if after a full charge, the same thing happens when the battery again hits that percentage.
Of course, if it's constantly rebooting no matter what you do, and at anytime, then the problem could be much deeper.