my guess w/ no evidence would be
~85% of ppl play qm regularly
~40% of ppl play hl (i feel like this is a highish guess but I dunno)
~20% of ppl play unranked
~10% of ppl play tl
~3% of ppl play ai
w/r/t queue time, for qm masters it's usually pretty quick but I'm pretty much always the highest mmr like scoobs said. it doesn't necessarily mean the games are skewed though
ive never gotten someone in bronze in my games afaik, unless it's mirrored on the other team, it's not that rare to have a 4v4 with ppl in ~300 mmr range but with the 5th on each team mirroring each other in mmr range a couple hundred above
my most uneven games are on my eu smurf, again I'd assume due to uncertainty. I only have ~80 games on that account but it won't be rare to have ppl ~2k mmr less than me on my team or against me. the team mmr is less even too, with teams often being ~200+ mmr more or less from each other. my hypothesis is either i need more games for mmr certainty or hotslogs is just way off on my mmr vs. the real blizz one and gave me too much. but at the same time, most of the time the team mmr for both teams are pretty close so i dunno what to think.
i dont expect new players to see long queue times, but that is also like the realm of uncertainty where they try to identify smurfs and in general don't trust your rating, I'd imagine there are more calculations and rules involved with newer accounts