Electrical – Why is the Bosch drill working intermittently

That is how it should work. The drill is designed so that less pressure on the trigger means less power to the drill. It could damage the driver if you were to keep it in that state of trying to turn and failing for an extremely extended period, but not if its momentary like you describe.

In short - good question but you're worrying too much. :)

Oh - yes - by the way - actually this is what it was designed for - exactly so. It's designed to apply torque to bolts and screws and drill bits.

This is symptomatic of a poor connection somewhere, or a bad-on-arrival fan. I'd rewire the switches using the screw terminals as a first step (don't forget to hook the grounds up when you do), and if that does not cure it, I'd try Craig's troubleshooting suggestion of switching the fan and the light. If the fan still acts up, then return the fan to wherever you bought it. If the light acts up when switched with the fan, then I'd say it's a problem with a connection.