980 Ti issues
That's a pretty high idle temp. Granted, I've never owned a 980ti, but no card I've ever had has idled that high out of the box, at least. I might raise that fan curve some, I have mine at 35%ish for idle.
I don't really see the base clock being on all the time as the likely reason for your idle temps, since actual gpu load rather than just clock speed is the real factor for temperature. My 970 doesn't idle at different temps when it's at it's 300mhz-ish low power mode versus when it's at it's base clock (because I have mine set at maximum performance most of the time).
Base clock issue might be a driver issue, since you have another probably driver related problem (the removable devices thing). I would use DDU to wipe drivers, then reinstall.
For the display issue, I don't really know. Maybe try displayport or dvi?
Wooooooow I'm an idiot... Reading some other FAQ's and they mentioned transcoding... Just realized I had Shadowplay on this entire time... *facepalm* Turned it off and it's gone down to 135 Mhz and 31C idle and 17% fan.
The removable devices thing definitely only showed up after installing the newest driver tonight. Might try a reinstall when I don't have to get up for an 8 am class the next day. 
And for the display issue, I don't have display port on the cheapest Asus monitor I could find at the time I built my PC. DVI definitely works fine but I use HDMI because I have external speakers plugged into the monitor and gets audio signal over HDMI. My backpanel 3.5 is taken up by my headphones. But like I said minor niggle. If someone knows a solution, I'll be quite happy. If not, then nbd.
Any ways thanks for trying to help though 
Appreciate it.