Question 2: I've seen an "unchecked" master doctor go off on his own to heal a sick person; never seen it happen with a trainee or adept doctor though.

Question 3: Master farmers are the only level farmer that can catch crabs, worth more food points.

Tech Levels:
Question 1: Each higher level of science tech gains research points faster. Not sure how much points per tech level per personal level.

Question 2: Villagers with level 2 medicine become elderly at 58