1) Haven't looked into the UT model yet. Will do and assumptions are definitely the starting point.
2) We are probably doing better than 50% just looking at how people are behaving. It may be showing up in the numbers this week as we've had a run of good days, but I don't think enough to call it a trend just yet.
3) If we are under reporting infected, it's a good thing actually. The way a virus spreads isn't exponential, it is close to a sigmoid:
If we are 4x further along the curve than reported cases show, then the transmissivity is less than we think and the growth rate function there at the bottom peaks lower. The math behind this is kind of hard to explain, but the slope of the sigmoid above flattens which lowers the overall peak of the chart commonly posted. And because we are saying we are further along than we are, it is shrinking the curve moreso than the usual flattening where it pushes out to a later date.
It also means that hospitalization, intubation, and mortality rates are 1/4 of what we think.
4) Same thing with long incubation periods or large asymptomatic cases. Most of the media takes that "omg, this is everywhere already" actually point to this being a lesser deal. I mean if it was everywhere back in February, then it really is flu-like as there have been relatively few severe cases until now. Adding a million "didn't even know they had it" cases makes this thing look more trivial, not more dangerous. It kills the narrative of those pushing it.
5) Most of the literature I've looked at avoids using the term "infected" as a category of people. There are exposed people (have the virus but can't spread), and infectious people (have the virus and can spread). If the disease is doubling every 3 days, and the incubation period is 6 days, then there are 4x as many exposed + infectious people as there are infectious people. But that's just semantics. There aren't really 4x as many cases. But I can't be sure that is what is meant when someone says "infected." It's one of those things lost in translation when scientific jargon gets simplified with no further explanation.