Does the absent parent have the same rights as a primary parent? Can they do whatever they want with the kids withought your consient? For ex... can they cut the kids hair if you disagree?

First they would not be an absent parent if they are cutting their hair.
They have joint custody and you have physical.
Legally I don't think you could do anything about them cutting hair but they should be decent and not do anything you do not want them to.
Are they doing what they want for spite or inconsideration?

First absent and present parents are not legal terms I am aware of.

You have joint custody, physcial custody, prminary custody, and vsitation rights.

If you have joint custody you have equal rights, if you don't have joint or don't have primary then no you don't.

Even if you have joint custody, you need to be considerate about the other parents feelings.

Now if you want some real help, why not explain exactly what's happening.

Why did the kid get a haircut? Did he/she need one? Look unkempt? Do you have a custody order or did you not pursue one after dad disappeared? You don't have the "ultimate" right to make all decisions for your child without one.