It most probably is the Psu (Cx series isn't well known for taking heavy loads such as overclocking etc). Just to be sure you can always test your gpu on another rig or borrow another psu. But in any case get a better PSU (SuperNova is good bet.)
Dont use Auto detect, Download the omega driver, uninstall all previous drivers. Shutdown your pc. Plug in your 280x and attach the monitor with your 280x. Now install the omega Driver.
a 550-600W PSU is recommended. I suggest you look at this teir list for a good idea about different psus:
http://www.tomshardware.com/forum/id-1804779/power-supply-unit-tier-list.html
Yes you will be able to play alot of current games at High-Very High settings with a 970 gtx since your processor is still quite good. The only thing which you should consider is if your Motherboard can Support the 970gtx (That is pcie 3.0 compatible)
If what you mean is your looking for "Msi" drivers, than you have to understand that all radeon gpus have "AMD" drivers aka Catalyst Controller (Latest is Omega) which you can download here:
http://support.amd.com/en-us/download
You can get other utilities like overclocking software which can...
If your motherboard and psu can support it, go for Crossfire (Keep in mind your case cooling and space between slots). It will give you roughly better performance than the 290 for good value. Other wise 280 is good bet.
Yes, it's recommended to re-apply thermal paste whenever the heat sink is removed (When the thermal paste is old). Moreover ensure good contact between the processor and Heatsink.
Ummm, I have a Asus Monitor, this happened to me 3-4 time when I turned of the monitor via its power button (At the front) I had to press it 7-8 times once, at different positions, before it turned back on. Try this, hope it works out for you.