A surprising amount actually.
Usually you outgrow/break the skis before you grind the base too much, unless of course you're some crazy racer who practices and tunes his skis every day but I doubt you ski that much so don't worry about it.
this is actually a decent answer, there isn't a universal limit or whatever, it all depends on your base thickness, your shop, how many damage you have done to it before bringing it in, how tall are your edges standing out, etc...
Depends on the type of ski. On a race ski that is getting ground a lot, you can be to the point that there isnt enough edge or base left to grind after about 10 grinds. The number can change a lot by changing setting on the grinder. Like the depth of the pattern in the stone, the amount of pressure put on the stones by the skis, or the amount of passes over the wheel. Chance are that you wont grind through your park twins.