Haven't had a CZ spring break (yet), but I had a Rem. 742 do the same thing as your pistol. Bang, Bang, click, click (with unfired rounds dumped into the dirt both times I manually operated the bolt. The last 3 coils of the firing pin return spring broke off, the firing pin speared them sideways and locked the firing pin up tight. That was a bear to get apart.
Cool spring story - when I bought a raggedy old Browning Auto 5 a few years back it looked bad but shot/worked just fine. I ordered all new springs for it, some new screws (to replace the buggered up ones) and a synthetic stock/forend for it.
When the parts all came in I started taking it apart to really clean it up good and replace the old parts. The magazine spring had broken at some point in that old guns life. Someone had taken a pair of pliers and bend the two broken ends around each other and put it back in the magazine tube and just kept killing ducks/small game with it for who knows how many years.
As far as CZ small parts go, I've ordered lots of them, just in case. Sometimes it just makes sense to order doubles of small parts. When something costs $3, or $5, or so, you might as well order extras and just put them away. I've been using those small clear tackle boxes lately, so I can see what's in each compartment.
Good luck with your CZ. The more I carry, shoot, clean mine the more I think I might buy one or two more.