Does the fan not turn too quickly for that? (edit:I’m being a muppet, that’s why you are using the pot of course – slaps head)
For the LED just a wee led and a 1 k resistor across the supply to the fan should do it
For the fuse I’m not sure I would bother. I would jam the fan and see how much current it takes but I wouldn’t think it would be much. Most likely problem is heat dissipation in the LM317. You don’t say what the input supply voltage is so it is difficult to estimate.
I confess in your shoes I’d have been tempted just to buy a 12V DC wall wart supply and connect it straight to the fan without all the gubbins or maybe just with a small cap across the fan terminals