Have you tried seeing if all the monitors show in AMD Settings? I think 3 monitors needed connected to an AMD card need amd eyefinity. Also would be worth checking if your gpu actually supports 3 monitors
I had similar issues with my R9 380X. Computer would freeze during games. Eventually died and had to get it replaced. Might be the same problem with yours.
shouldn't damage if you have a surge protector or something similar. As long as the system isnt updating anything when the power cuts of it wont break
Why is there a power outage every day?
Depends what you are using it for, I wouldn't get an R7 240 though, its not much better than the integrated graphics on the CPU. Get a better CPU with money you save.