That 10 second thing should be fixed if you run an update
(It'll bring in a ton of packages actually, but one of them will fix that stablilization thing.)
As for time. After unchecking the thing, make sure that the file /etc/adjtime file says LOCAL
If it doesn't, then manually edit it, changing that UTC to LOCAL
Now, I've only run into this with Ubuntu, because their standard CD doesn't give you the chance to choose whether it's local or UTC. Fedora does give you the chance during installation, but many people miss it.
The thing is, that it will set the system (that is, the computer's BIOS) time to its time. So, assuming it works the way Ubuntu did for me, do this. (If it doesn't work that way, I'm only costing you a few extra minutes)
Set the time to local as you've done, and then check that /etc/adjtime. Assuming they're both correct, and that the time is also set correctly on your system, shut down.
Now, when you boot up, before going into Fedora, go into your system's BIOS and make sure that the time is set to local, not UTC. What I found with Ubuntu (and with that, the only thing to do was edit /etc/defaults/rcS) was that even though I changed it and reset the time, it would still, before one reboot, set the BIOS to UTC.
So, once your BIOS is definitely set to local time, hit F10 to save its settings (as a rule, anyway, the majority of BIOS use that as save and exit) and boot into Fedora. The time should be correct.
Then, boot into WIndows and make sure that its time is also set to local. If not, and you have to change it, then do so and again reboot, again checking the BIOS. (I don't know if Windows will reset the BIOS time or not.)
Cumbersome as that is, it should fix the issue.
(In general, during installation, you choose to uncheck the box--similar to what you're seeing-- for UTC, which is the default., then you odn't run into that particular issue.)
Hope this helps