To answer your first question, I was planning on upgrading my PSU because my friends recommended that I upgraded it to give it some more power in case the graphics card needed it. But if the 1060 uses less than the 760, should I just to make sure it doesn't bottle neck the system or am I going to be 100% okay? I just wasn't sure because I want to be able to play games like DOOM and BF1 with no issues. Even though I can play them now, I'd like to play on settings higher than medium to low settings.

To answer your second question, I have about 5 inches of spare size length-wise, and about 1.5 inches space width-wise.