I would also check the alignment of the pulleys on the stepper motors and the belt. The belt should ride in the middle of the pulley. I had to adjust mine after i installed the belts. You may also need to increase tension on the belts. I personally use 3D printed belt clamps vs the stock one to make the belt more parallel.
The fan on the laser is fairly loud. There is no speed adjustment that I am away of. You could replace the fan with one that has better bearings to quiet it some. The beam firing when unplugged in not normal but I have heard of many safety flaws with this machine. Mine will fire on high power as soon as I connect the USB cable to my laptop. To prevent this I make sure to have the button on the laser engaged. Once I am ready to engrave I have to remember to hit it again before starting the project