First thing to do is to check phasing between ALL mics & loudspeakers. Maybe ask someone professional to carefully do it, because full description of this process would be long and hard to understand for you. Phase mistakes can be everywhere - mic, cables/wires, mixer, amps, crossover, loudspeakers, even effect devices, direct boxes, instrument amp connection & miking, drum miking, etc. Digital equipment & wireless microphones make this latency/delay/phasing problem much more complex & deeper. Go analog & wired for such simple system. If there is something fully or partly (turned phase) out of phase - increased feedback is "normal" thing... Most low-mid level audio systems contain phase mistakes...
Good signal source, using of microphones & loudspeakers with adequate directivity and sensitivity, right microphone & loudspeaker placement is second thing.
Right equalising is third thing. If you are doing it - try to equalise generally to cut side, and compensate it with gain. It is pro "law" for main & monitor, channel & all other equalisers (less distortion and phase shift). Equalise sound system first (using point of reference recorded signal), mixer channels second. Do not fully trust to audio analysers for system equalising, just use them for "side" information about resonance peak frequencies. Do not equalise them, but look for reason of these resonance peaks first !
Concerning room - orient loudspeakers possibly diagonally, not parallel or perpendicular to walls, ceiling & floor - it will reduce reflections & resonances of room. Use upper corners - it will increase sound pressure and cover listeners. Do not hesitate to pan signals wider in stereo for stereo loudspeaker system - it is better as mono signal from two placements. Use one room corner & summed in mono signal for subwoofer - it will provide more sound pressure and right phasing at any point of room.
Right handling of vocal microphone is important, never close rear side of directive capsule (mic head/wire ball) by hand, it converts mic to almost omnidirectional, & increases feedback possibility many times, hold microphone under some angle in case of close use.
