Question

Just number five!!!!

Answer 1

The smallest nonzero current depends on the maximum time T you are willing to wait. The smallest current would be I = e/T. After time T, one electron is observed to pass through the given area.

Answer 2

Clever question.
Current = (charge)/(time).
The smallest possible charge is the charge on a single electron. But then the current depends on how often one electron passes you. So there's no smallest possible value.
Of course, if the current is AC, then it's negative for just as much time as it's positive, so the AVERAGE of an AC current is zero. You can't get any smaller than that.