1) Semantically Ambiguous??

3) In this case the number of balls might be indeterminant, or might be zero. - I think we are saying its zero.

However, for those who think its infinite, how about this induction:

n=k=1
Ball 1 is taken out at action #1
=> True for n=k=1

n=k+1
Ball n is taken out 1/n(n-1) minutes after ball (n-1)=ball k is taken out
as ball k is taken out (proved earlier) => ball n is taken out.

=> For all n in the set of integers (which all the ball numbers are), ball ne is taken out, and so is not in the box at the end.

It is an interesting question though, isn't it