1. The mags should drop free, but it's not unusual for the CZ-82/83 have them binding on the grips. Remove the grips and try releasing the mag. If it drops freely, you've identified the cause. A little shaving of the inside of the grips can solve that.
2. Hold the trigger all the way back and you can push the hammer forward and hit the firing pin. Some are concerned that they can't see the hammer hit the pin when pulling the trigger, but it does--too fast to see it. Like Joe says, empty the gun, drop a pencil down the barrel and pull the trigger. Make sure it's pointed in a safe direction first! I stuck a pencil in the ceiling with my -82.
3. The mag release and single-screw grips are the design flaws of the 82/83 series. Plan on the grips working loose during extended firing. Locktite, O-rings, lock washers are but a few of the suggested fixes for the grips. As for the mag release, I've never heard of "loose and rattley." But yes, they usually work like crap or badly in one direction or the other. My -82 is very difficult to thumb release, but the mags release easily with using my forefinger.
