I use Asus M/B's and they come with a piece of software called 'fanexpert' which lets you manage fan speeds versus temperature of the different sensors on the board. Without this, the fans are always running at 100%. I would imagine that Gigabyte has an equivalent.. I would start by looking in that direction.
Secondly, you say that you can hear " squeaking noise near the CPU area " generally speaking, noise from a PCB like a motherboard may be an indication of faulty capacitors since they are among the only parts that I know of that can produce audible tones when damaged. Just to be clear, do you hear these sound when there is NOTHING plugged in the audio ports? because many on board sound cards produce parasite sounds from other areas of the motherboard: I have an Asus P8P67 that has horrible parasite sounds like this; including sounds associated with mouse movements as described but they come through the speakers, not the M/B.
Hope this helps.. good luck with your issues
