I would say that your fan squeak is the key to the problem.
The bearings are tight, and need lubrication, hence the squeak.
The tightness of the shaft increases the electrical current needed to run the
fan, which inturn overloads the fuse and it blows.

You will need to free up the motor bearings for this problem to be fixed.
You will have to get to the fan motor to do this which is no easy task I
believe.
A bigger fuse may enable the fan to run but I would not recommend this as the
whole thing is going to get hotter and get worse.

Sorry to be the bearer of bad tidings.
Steve Cotsford