Are you using a PS/2 keyboard? If not please do, or enable Legacy USB / USB Storage in the BIOS.
I had a keyboard that would cause the same issues you just described freezing in the BIOS, it was due to incompatible USB Keyboard with the BIOS which they have now corrected.
Yes please disable ErP and then in the morning see if everything is still reset and or time is way off as you describe. That all sounds like ErP is draining your CMOS which I have tested and reported to be an issue with no fix in sight as they say the can't replicate the issue. Here is the latest thread with our testing and my reports from Gigabyte in case you wanted to overlook our thoughts or testing results with EuP / ErP.
http://forums.tweaktown.com/gigabyte/38267-x58a-ud7-settings-reset-after-shutdown-win7.html*Edit*
In regards to your post, as you posted at the same time as me, I bet it's your USB Keyboard if you were previously using one.
And for the restart instead of shutdown.
If you have Turbo Enabled in the BIOS please disable RAID. If you use RAID and need Turbo, disable Turbo and set the multi to the max value you need.
You can either set 21 with Turbo disabled, or set Turbo enabled with 20, but with Turbo enabled you need to disable RAID.
Battery is facing the correct way I'm sure, if you want to check just be sure you can see numbers and or letters (KTS CR2032) on it, if so then it's installed correctly