1965 Ford Fairlane clutch problem

Nice view. You should be able to put mustang parts into your fairlane. There will be minor differences, but probably not a lot when it comes to clutch and pressure plate.

It sounds like your clutch is "chattering". It's either severely worn out or contaminated with oil. The best repair would be to have the pressure plate resurfaced and the clutch plate and pilot bearing replaced. Those are the things that need to be done (minimum) for a clutch job.

Other things to replace are are the throwout bearing, transmission shaft seal, rear main seal, and if you really want to do a heck of a job, replace the two freeze plugs on the rear of the engine as well.