Just flashed the 4.4 firmware. First bootup was hell, everything was too slow. But after rebooting, everything seems to be smooth again.
Reboot after inital update. 1-2 reboots wouldnt hurt.
I belive it is impossible due to aspect ratios being different. If you really want 13mp at 16:9, the image would probably have to look stretched
For the Google related problems, you could try going to Settings>Accounts>Google and then Remove account. Clear the cache and data of the problematic google apps, and then sign back in.
For carrier related problems, reverting back to your old apn...
Sadly, nexus7 does not have an mhl usb port and miracast didnt pick up. You could still use chromecast to send videos to your tv
Link to 4.3 Android for nakasig(3G)
just replace the correct files in the instructions