As far as I know, with the exception of the latest model slide release levers, the CZ-83 parts all fit the -82 and most (if not all) are available thru CZ-USA.
Are you sure the slide is returning to battery on the last rounds? Sounds like a very odd issue. I'll have to get my 82 out and experiment to see If I can duplicate. Usually a gun mechanical problem is consistant, not something that happens on every certain number round. Mag problems not so. Did you disassemble and clean the mags also? Mine were really full of gunk when received. IF you're planning on lubing them, I suggest using a dry lube only (NEVER WD-40) so it doesn't attract residue so bad. The top end of the mag is bad to collect residue. I break down and clean my mags about every other range trip.
Somewhere in SailorCurt's site, during reassembly, it tells how to make sure the sear and hammer block is working properly. Might give that a try.
I'm starting to suspect, given the price you paid for the gun, that someone may have torn it down, couldn't get it reassembled correctly, and sold it for parts or trade. I'm thinking that if you do a complete disassemble, clean, inspect, and reassemble, unless you find something broken, it will work fine.