If you had a fan blowing out the window, it could slightly reduce the density of the air in your house, leading to a tiny increase in the speed of light through it, so that would make the waves technically faster, but by a vanishingly small margin
It wouldn’t increase the bitrate of your router at all, so it wouldn’t make a difference, but the waves would be faster
Yes, but then it’s slower for your computer to talk back to your Wi-Fi, so it ends up cancelling out