How To Tune Room / adjust Settings After Taking Measurments

Acoustical measurements (RT60, ETC,) would only be of use if you intend to apply acoustical treatments to the auditorium.

You don’t need REW to ring out the system, which typically refers to EQIng the vocal mics to prevent feedback. That should be done via the mixing console on a channel-per-channel basis, especially if multiple brands / models are in use. Every mic brand / model will feed back at different frequencies; it makes no sense to EQ the entire system based each one’s unique issue. IOW, if one mic needs a cut at 4kHz and others don’t, it makes no sense to affect the sound of all the others based on that one. Or the reverse. And so on. Most mics will feed back at one frequency. Any decent mixing console made in the last 30 years will have one or two sweepable EQ filters for each channel that can effectively deal with it. It's not hard to ring out the system in real time - in fact, that's how it's typically done. You don't need REW for that. Typically you only get a mic ringing at multiple frequencies when you try to push it to insane levels, or if it's too close to a speaker.

If you have to resort to using the main house EQ for feedback control, it’s better to use a parametric EQ, as they are more precise than graphic models

The main thing REW would be helpful with is setting up a new installation, to adjust the levels of the amplifiers in a bi- or tri-amped system for a proper blend. Unlike residential systems, auditoriums typically don’t need much of a house curve, if at all. When it sounds best, there will be very little (if any) elevation of the lows – i.e. almost flat response (measured with REW).

Once that’s accomplished, you can run REW to see if there are any glaring discrepancies in frequency response that need to be adjusted. However, if your speakers were made in the last 10 years or so, they probably will sound pretty good and won’t need much (if any) EQ, unless perhaps they are bottom-of-the-line model.

Regards,
Wayne

REW is pretty much an ElectroAcoustical Laboratory. Interface- Line In to Line out it can test electronics. I spent most of my Live Sound Decades using a Chilton QM3. BBC/Neve type of thing with Broadcast type Eq. My speciality would be Acoustic Bands. On a tour I would typically focus on the Lead Vocal Mic, flat, to find the resonances to Eq out using the trusty Klark Kent Graphics..... Periodically checking with all the mics on. The Waterfall and Spectrogram graphs in REW show resonances continuing over time. This makes deciding what to do about them easier and more sophisticated. I often used AKG C535, which was a very early vocal condenser. If the Band, Singer were unknown, I might use an SM81 for it's neutrality, flatness.
I agree with Wayne that a pretty flat response is needed in these reverberant spaces to cut through. Rather than the warming domestic Target Curves such as B&K or Harman.