They increase the amount of plunder/Money you recieve when you farm or just hit. Also in war if you have a high TB: It can be very hard for people to hit you.
Tutors can give you a bonus to your stats that help with battling. The more money you have in tutors the better. You wanna get to your max plunder. Getting your max plunder will result in you gaining more from farming. I think you need $15m for every 2kcs you have
Gives you extra intelligence/strength bonus. While you're attacking someone and it increases your winning chance to winning a battle. It doesn't give you extra stats.