(a) Should these considerations modify your confidence or anyone else's that you have in fact found your keys? If not, why not, and if so, what correction is required?

a) Yes - these considerations should have an impact on your confidence. However, this being a evolutionary familiar scenario, your intuition has already made the necessary adjustment such as correcting for multiple comparisons and all the other hyper-complex issues, so don't whip out a pencil and "correct" yourself..

b) Yes.It is not always negligible. For example, if you were searching an entire apartment complex with identical doors for your keys and you found one in the hall you'd check the key against the lock first to see if it were yours before locking yourself out. Or, you might ask your roommate if they had their keys, to ensure you didn't accidentally steal it. The considerations can alter your certainty.

Once the lottery results are out, do you check your ticket? Why, or why not?

a) I am weighing opportunity cost against potential winnings and you did not say how much the prize was or where I got the ticket from or what the URL was and if I recognized the domain name. (In practice, I don't actually check the bottle cap codes on soda or follow up on coupons making similar offers.)

b) My intuition is automatically factoring in estimates for pranks, scams, matched tickets made in error which were not honored, and so on. If a smarmy guy in a suit standing around handing out URLs promising money, or if cameras are hiding in the bushes...

c) See (b)....What's the lesson here? I don't think I got it. Mine would be "we automatically do all this stuff in non-abstract scenarios".