As far as I remember in the cartoon, she was holding an armful of hair with her hands, and even throwing a ring over some object ... So it is quite possible that the hair itself will support such a weight ...
As a child, I watched some kind of program about experiments (I could not find it, alas), there they raised (!) a whole car (!) with the help of a wig made of natural hair, but, unfortunately, if you decide to lift something significant with the help of your hair, then your skin and the hair roots themselves will not withstand such a load.
In theory, yes. But if they are fixed on the top by something that is able to hold the weight that the one who will climb on them has. Otherwise, there is a risk of losing them simply because of the load imposed on them. Also, I guess it will depend on the structure of the hair. For it would be difficult to climb to any height by scattered curls to any height. If they are hard and straight, it is suicide.