We do know Boeing bid the price so low that it probably overrode or devalued other parts of the evaluation, literally an offer too good to refuse...
I mean there are a number of ways to achieve this, especially while still hitting high-performance targets, the most "conventional" of which and the one Boeing is most likely to do (and being one of the few that could even afford to do this, at least before COVID-19) doesn't even involve any engineering at all: just eat any costs that comes from severely under-bidding in the hopes of greater long-term gain, especially with increased market share, or even just to squeeze out competition entirely.
That said, designing a non-stealthy, somewhat supersonic small trainer isn't too hard. I'm surprised they were able to undercut all competitors since they've already been in service and production for a while, but all of those designs are also designed for significant combat capability; the KA-50 and to a lesser extent the M-346 aren't really designed to be trainers in the first place but rather legitimate fighter-bombers first, THEN trainers second. That requires a bunch of added-in capability that drives up costs in a hurry, even if the KA-50 is almost literally a mini-Viper (in fact in some ways especially so). It seems like Boeing's entry, nee T-7A Red Hawk, was designed to be a low-cost affordable trainer and ONLY as a trainer. That does significant hurt its export potential, but that's a moot issue if Boeing only cares about the USAF contract in the first place. Clearly it majorly paid off.
Also don't underestimate or forget Saab's contribution. Even though it's a standard configuration I have to wonder how much of this thing is really just a Gripen with conventional tail planes and all of the combat capabilities "dummied-out" and then seriously shrunk. That could explain both the rapid design process and its cost-effectiveness (and probably the T2W ratio too).
But also I'd really like to know how the other entries failed the high AoA requirement. That seems pretty basic to me.
Are there a lot of composites on the T-7? I was under the impression that it was nearly all metal? Not sure why, I cannot recall anything definitive.
That really depends on application and specific type.
Materials-wise, composites should be extremely cheap, theoretically. Carbon and Silicon happen to be some of the most abundant periodic elements to exist in some non-gaseous form both on this planet and in the grater universe itself, and the other key ingredient for hydrocarbons, hydrogen, is the most abundant periodic element in the universe period. So it's not because the stuff is rare. Incidentally aluminum, one of the most expensive metals commonly use in mass-manufacturing (and of course also relevant to aerospace), also happens to be the most abundant metal naturally occurring on the parts of the Earth humans can actually get to.
The big issue, at least for now, is manufacturing, but also to a lesser extent actually getting that carbon. Most carbon used for manufacturing is derived from fossil sources which are still at least considered to be cheap and plentiful, but turning a barrel of crude oil into a "carbon-composite" solid structure useful or an engineering application is the really difficult part, as I understand it. Yes, I'm also well aware that I also just described the process for manufacturing plastic goods which are so extremely cheap in some cases it's actually problematic, but what separates "carbon composites" are getting proper molecular alignment that makes it far more durable than most cheap plastic goods and for that matter, most consumer-grade metals. That's a major issue with manufacturing that needs to be overcome.
It should be noted that silicon composites don't really have this issue. Fiberglass fuselages are cheap, or at least no more expensive than all-metal ones, and seem to be giving exceptional service in kit-built and certified aircraft (and also make up many common "composite" components on airliners and supersonic military aircraft, including no doubt the T-7). What would also be a potential game changer is cheap space mining (from asteroids) of pure carbon, which potentially could dramatically decrease carbon composite (and plastic) manufacturing.