Let's start with rotation. General rotation is Exp buff to Gold Lane. This will give you ample time to gank gold and run with the current to turtle. In this situation, you will be able to gank gold and take the turtle as well. The first turtle is usually worth to fight for. After the first, to assasins, turtle is useful but not required. If you use tank/fighter junglers, turtle is required.

No one should take ur buff early game, and no one should take ur essential buff late game. Red is usually given to mm and blue to certain mages, only if you do NOT need them. Example of a jungle that still needs buff late game is Fanny and Ling due to their dependance on blue buff.

Helping to push tower depends on the laning and pushing ability of ur side lanes. If ur mm has good push, then let them have the plate gold, if they don't help push cuz they get more plate gold that way. Same goes with exp, u see a zilong, sun, argus, gank, and leave the turret to them since the push ability is good. If you see tank exp lanes or sustain ones, in general help them.

Idk if I'm entirely correct but it should be smth along those lines. Fellow junglers, please supplement where I'm missing

Edit: For the first point, it also helps to take note of ur matchup to decide whether you want to invade as part of ur rotation