Without knowing where you live, it’s difficult to say if $85/hour is excessive for labor. Some places just cost more than others. A single apple goes for about 3 bucks in Jackson Hole, after all 
It’s certainly possible that he’d know what kind of clutch you have - he is after all a mechanic and sees cars all day long.
I think if you drive a car with a slipping clutch, you know whether or not it’s slipping within about the first 30 seconds of the drive. You don’t need any kind of diagnostic equipment to determine whether or not it’s slipping. If it has the symptoms you described, it’s slipping. If it doesn’t, it’s not.
The 21 point free diagnostic is, frankly, BS. They do this in order to find stuff wrong with your car so they can charge you to fix it. They don’t need to do that with you because you came in already knowing something was wrong with your car, and they figure they’ll skip the BS step and go straight to the charging-you-money step.
Their price for parts sounds kinda high to me, but it could be that Mazda clutches are more expensive than other cars. I will say I spent $900 about 4 years back to have a clutch done in my MR2, and just about everything on that car costs more than normal cars. Your estimate seems a bit too close to my estimate considering you’re driving a more “normal” car.