Is it possible to use a Campagnolo bottom bracket with ordinary shimano cranks? Shimano 600, the ones with a square hole... And / or can I use a Shimano axle in a Campagnolo bottom bracket?
In general no.
As sydney says, the spindle tapers differ - depending on the age, Campagnolo tapers may be their own proprietory design (similar, but not identical to, ISO), wheras Shimano use JIS - the difference is that whilst both use a 2 degree angle on the taper, the length of the taper differs as does the size of the "starting square" - ISO is smaller than JIS so if a JIS crank is fitted to an ISO (or near-ISO) taper, the crank tightens too far up the taper.
At best this will result in a chain-line that is not optimal unless this is catered for in axle length selection, at worst the crank may tighten so far up that the fixing bolt bottoms the crank out against the back of the bolt washer, or the crank migrates so far up the spindle that it is drawn hard against the shoulders of the taper. Either way, the fixing of the crank is compromised and in the latter case, crank failure is common.
Mixing spindles and cups is a real lottery - the contact angles of the spindles and cups have to match, plus the shoulder width on the bearing surfaces of the axle have to suit the thickness of the BB cups as otherwise you may not get the desired offset on the gear side, or the adjusting cup may not screw in far enough, so possibly causing BB thread failure - or may screw in too far to allow the fitting of a lock-ring.
"Back in the day" experienced mechanics would sometimes combine BB cups and axles from different manufacturers but there was never a matrix of what might work with what to produce result "x" as the number of possible variations was enormous - it was largely a matter of trail and error and memory (I speak from experience ...) and not to be recommended - it was always the least-favourite option or more commonly, a work-around to try and solve some other problem ...
Your best bet with a Shimano 600 crank set is a sealed cartridge bearing unit from Shimano or some other JIS maker ... UN52 in the Shimano range (if you can still find one) has an excellent price to quality ratio. If I recall correctly you will need around a 113 mm axle, although that will depend on what chainline you are trying to acheive.