Very generally speaking, all CNC machines should use GCode - which are literal instructions to the machine about where to move in sequence, for example:

Move quickly to X=10, Y=0, Z=10
Turn on the spindle
Move at this feed rate to Z = 0

This is the set of instructions which the CAM program makes. The controller on the CNC is responsible for enacting those instructions precisely.

If you buy a used CNC, it should be able to take these instructions from any CAD program. It may also have some manual offline functions as you mentioned, but they will be machine specific.

Now, replacing the cathode screen. This is likely to be a can of worms; it probably won't be just a standard interface to swap out (it might be, but certainly don't bank on it). Often, if there is any problems with the machine controller it's worth considering ripping it out and rewiring the entire thing with a more modern controller - but this gets very complex and expensive very quickly.