1) I know in my flight school we were shown, but realistically during GFPT you dont need to lean the mixture very much. We did it on the ground during taxi so as not to foul the plugs, but once airborne we rarely went above 2000ft (only for stalls).
2) Yeah this is odd.
3) The rule I was shown was 1 extra minute per 2000ft climb. So climb to 9000ft, add 5 min to your cruise fuel. On a 172, it works out pretty close, esp with all the variable fuel reserves and margins built in.
4) I can understand the logic, but I think students need to practice lodging flight notes, as it is tricky when you first start.