Re: Advice for dealing with singers who wander out in front of the PA
"I want to cut, Master! I want to cut!"
Okay, not self-experimental surgery.....
Gigs are the best and worst places to experiment. If you screw something up... well... uh.... But if you fix something or find The Lost Chord® in the FX unit, you're a hero. The pressure is great.
Much experimentation can be done with headphones; a mic and your voice; a playback device with music and pink noise, and your mixer. You can experiment with dynamics processing (compressors and gates) and time-based effects like chorus, flange, echo, doubling, reverb, etc. You can give a good listen to how your channel strip EQ changes your voice or affects program audio. If you record some individual instruments at a rehearsal, you can use the recordings as source material in your experimentation. One of the great things is you can learn without needing live players for this part of your training.
Some of what was alluded to about compression potentially altering your Gain Before Feedback is based on "make up gain" that is applied to compensate for the level reduction caused by the compressor. That gain is *always* there, even when the compressor is not lowering the level. When the signal is above threshold, there is additional gain. If you plan for that, factor it in, etc... (and most importantly, sound check with it set the way you'll use it in show) it won't inherently bite your ass, but if you're in a situation where extra level causes feedback you could be in for a long night when the artist needs "more".
Connected with this issue is that in most small analog mixers, the channel insert point is almost always "pre-aux" even if the aux itself is switchable 'pre/post'. You'd be applying the same make up gain issue to the singers monitor wedge and introducing a paradox to the vocalist: singing harder and louder but not hearing herself that way in the wedge. There are anecdotal stories of singers "blowing their voices out" and I suspect most of them are greatly overstated... but the extra strain of singing against a compressor is something a vocalist probably doesn't need. This is something you can experiment with over headphones. Sing into the mic and get your -6dB of compression and then really lean into it. Imagine singing against that all night. 
You mentioned gates, too. In your vocal application gates are a gauze pad applied to an arterial wound. Here is a piece of wisdom, bestowed by The Old Soundman (or someone like him): "Loudest sound at the mic, wins." You need to convince the band that less stage volume is manly, artistic, and will get them laid. What instruments are bleeding worst, or is it everything?
A final prognostication: you are pushing the rig very hard to get the vocals and a couple of instruments above the stage levels. You need so much gain (Needed Acoustic Gain) to get over the din that there will be the potential for feedback any time your singer walks in front of the PA.
