You should check out Berkeley's deep reinforcement learning course[1]. There's lecture videos, slides, and homework assignments, and it's all very up-to-date.
My Japanese is fairly fluent, but the guy around 08:00 is pretty much totally incomprehensible...
The later dude at 10:00 seems to be announcing lot numbers ("16-ban"), doing the auction in ten-thousands ("75" for 75,000 yen?) and then announcing the winner ("Ebisuuuuu!") before going to the next.
Yes, it happens at compile time. To understand how proofs work here, you want to look at the Curry-Howard correspondence. Basically, there's a correspondence between types and propositions, and between the values inhabiting those types and proofs of the corresponding propositions. So a proof looks like a value of a certain type.
[1] http://rll.berkeley.edu/deeprlcourse/