In those cases I would need to check that they are the right keys after finding them. Everything else (part 1) remains the same.

For the lottery scam, well, I was assuming I had heard of the lottery. This is very likely since IIRC the only legal lotteries here are run by the state. The exact answer depends on too many contingent details. More importantly, it does not strongly affect my actions - I am going to be careful as anything with receiving that money - I'd visit the bank and make a new account to put it in, say, even if I'm 90% confident that it's legit.