1) well in a way it is a half truth, a cop out/what the fuck?! moment all the same though. they bonded during the film which ofc would build up trust, thus the "last time i trusted someone" line =)
2) i'm about... 50/50 with this tbh, it could make sense on the ground as it would explain how bloody fast they could mass produce those tesseract infused weapons in such a short amount of time between thor and avengers assemble, and when asked the "why" instead of saying "we knew about this years ago" they shifted the blame to the gods of asgard so that old can of worms wouldn't be opened. that's how i saw it anyway
3) wasn't that agent carter who made the name up?