To respond to a few of the questions regarding the sound engineer (s), given my limited knowledge of this whole topic, but it looks like I may know at least a tad more than previously mentioned, so here we go:
Adam has his own monitor engineer (Gary Stokes), who needs to be and is very familiar with Adam's hand signals, wishes, etc. The monitor engineer does not belong with the venue, he is somebody that is part of the tour and therefore on the road with everyone.
I am noticing that at least on the official listing, Queen only lists one monitor engineer for the whole group, beyond Adam's personal one. That would be for 5 band members on stage, plus all their techs. I have no idea how that works. Even if not all members are using in ear monitors, there needs to be feed provided to the different parts of the stage via a stage monitoring/ foldback system.
Maybe Q3 found out some details during her various backstage tours and can fill in some extras. I cannot.
In addition to the two mentioned positions, there are plenty of other people who make up the audio team for this tour:
FOH audio engineer
Audio crew chief
Audio system engineer
2 PA technicians
These people are all part of the 'traveling circus'.
At every venue, they will have to interact with whoever is the local audio specialist for the venue. I have no clue how many people that team typically has. I also don't know how much of the whole PA system travels or whether certain parts are mobile and they plug into locally mounted larger speaker systems at the venue. But there must be quite a bit of stuff traveling rather than stationary, to require two PA techs on tour, I would think. But as a lay-person who knows silch about such stuff, I admit that this did surprise me. I thought that at least for FOH, a majority would be local. I guess, little did I know.
Regarding the interaction between Adam and monitor engineer, I have so say, that I am a bit stunned at all the reports about Adam 'yelling' at the sound engineers, etc... While I have read this repeatedly on fan boards, multiplication of such information does not constitute fact for me. It goes against my observation of Adam's overall personality and general behavior on stage.
What I have seen, is that Adam, after being unable to resolve his issue with hand signals, left the stage, to do what needed to be done. I recall two times, where this had to happen in such a way that it was actually disruptive to the performance, and obviously, no performer would choose to do that, if not absolutely necessary, and of course this would make any performer majorly unhappy. But in no way, did Adam have any outbursts or anything.
I am not familiar or don't seem to recall this Washington DC event, you are talking about. During the Marriage Equality concert he had problems and had to talk to sound guy during concert, but that was a 4 song part of a larger event kind of thing, so most likely, he did not have his own monitor engineer there. But I also don't understand how he could have possibly 'fired' somebody. So, I really don't know where this comes from and would love to understand where and for which concert this supposedly was. This does not make sense to me.
The monitor engineer is a sensitive job. If he/she dials it up to much or wrong, he can hurt somebody's ears or create a very unpleasant soundmix directly into the ear. Not a pleasant idea - lots of trust involved with the job, and I am sure, having to rely on somebody unknown is not easy. Must be a difficulty at a lot of these one off events for all artists that are not big enough to employ somebody for this position on salaried basis, just for themselves.
But at least for this QAL tour (and btw also for GN tour), Adam did have a monitor engineer who was traveling with the tour.
Hope that answers at least a few questions, and it probably also raised a few, so let's see whether somebody can talk more specifically about those Washington DC events.
Love your story, and love the Britney Spears part!! 
