With regard to the phantom power issue, there is either a problem with the wiring, the microphone, or the mixer.
As others have suggested, eliminate variables one at a time.
Does the effect happen with different mics on the same channel? If so, it's probably not a problem with the microphone. If different mics behave differently, it's probably a problem with the mic.
Does the effect happen when you bypass the wiring (and/or using different cables)? If it's always the same regardless of the wires/cables in use, it's probably not the wiring. If changing the wiring changes the behavior, you've got a problem with the wiring. (If your wiring starts with the shield/ground on pin 1 at the mixer and connects it to pin 2 or 3 at the jack, that can cause problems, though right now I'm not sure how the problems would be manifest. Swapping the wiring at pins 1 and 2 is an easy mistake to make.)
If you prove the microphone and wiring don't make a difference, it's probably the mixer.
As for the feedback, gain structure has nothing to do with feedback. It doesn't matter where you get your gain. It's the total gain that matters. The way to eliminate feedback (to maximize gain before feedback) is with proper microphone selection, relative positioning of microphone and speakers, proper microphone technique by the talent, proper equalization, and room acoustics. Room acoustics is usually the most difficult to change, but it is by far the most important factor. But gain structure has nothing to do with feedback.
(The only way that gain structure will affect gain before feedback is if some gain stage in your mixer is nonlinear, where it boosts some frequencies by a different dB than other frequencies. That is an indication of failure or poor product design.)
What gain structure DOES have to do with is the noise floor of the system and clipping. Proper gain structure minimizes the audible noise in the system while still preventing clipping. This is known as dynamic range. Proper gain structure also ensures that all inputs result in the same ouput level when the channel fader is at a given point in its travel (i.e., 0 dB) so that your mixing becomes visually intuitive -- so you can tell the relative levels of each channel just by looking. If your guitar is at -10 dB and it's drowning out the vocals that are at +5 dB, you may not have proper gain structure, because at a glance one should be able to tell that the vocals will be louder than the guitar (not considering program dynamics here).