After the update, be sure to manually default the cameras settings, then press and hold the hard reset button on the side of the camera for about 5 seconds.
Sounds like it's connected properly if it enters and exits parking mode correctly.
All parking modes will consume power. The draw between the different modes is minimal. Newer cars computers systems will alert you of a power draw, so I don't think there is much you can do here, unless you...
The cameras settings default automatically when changing firmware, but manually defaulting the settings in the menu should be done as well. Did you do this? If not, you should. This will ensure there is no leftover values from the previous firmware messing with the new firmware.
Be sure to manually default the cameras settings in the menu (it's an option in the menu) after any firmware change. You should then also press and hold the hard reset button on the side of the camera for about 5 seconds.
Sounds like a poor cable connection or bad cable. Make sure they are fully seated. It should take some effort/force to get them to seat properly. When properly seated, they should not be very easy to remove.
Also, the SanDisk Ultra cards are not a good choice in dash cameras. Get the SanDisk...