There isn't a minimum distance. The feedback depends upon many things, in essence the gain in the loop created by the speakers/air/mike/amp/speakers. It can be affected by changes in any of those.
The type of mike probably will change the feedback, as the gain and directionality of the mike will change.
If it is a major issue, you need a feedback preventer, which is (I believe) basically just a frequency shifter - shifts all sounds by a few Hz.
another thought...try cutting the very top and bottom end of the tonal spectrum a bit, i have found this has helped make the best of a bad situation a few times.
Dynamic and phantom powered mikes won`t affect the feedback issue, the xlr leads reduce rf pickup and other nasty interference over longer cable runs thats all..