For min cut only the value at the cut matters. So you can have multiple cuts that are min cuts. The number of points included don't matter.
Depends on what the question is asking. If you are suppose to use a specific algorithm to find the min cut, then you should give the solution provided by the algorithm.
You can also provide all the possible cuts just to be on the safe side. Also, you should have some justification that no other cuts can have larger value than the ones you found (I think this is the most important part).