Just buy a $30 Hyper 212+ or EVO. They'll come with thermal paste and be much, much quieter. (And will use larger fans; the small fans that'll fit on a stock cooler aren't going to ever be that much quieter than the stock fan.)
^what he said. The problem is more the heatsink than the fan anyway. A larger fan on that heatsink would likely be WORSE because it would block more if the center and pull air AROUND the heatsink and not THROUGH the heatsink
Hehe, good job.
(Don't worry, we've all seen worse.)
The motherboard tray is what your motherboard is actually MOUNTED on - often it's a piece of metal between the back case and the rest of the case that you put the motherboard on so that you can hide cables behind it and install coolers. (Many of them have holes where the CPU sits so that you can do that.)