Spaying will indeed help that playful biting. Encourage the others who live with you to adopt the same method you did to discourage the bites. She sees you as alpha, but doesn't seem to recognize that the other people are going to be alphas too.

Often a shake can (coke can with some pennies inside) can both deter the biting and going out the door. If you can keep one inside the door and outside the door that would work best. As you leave or enter, shake the can until she moves back. When you enter the apartment, don't acknowlege her until you get about five feet away from the door. Then give her a treat and some petting. Do the reverse as you leave, treat and petting in the same far-off spot. This will establish a greeting and leaving ritual.

Unfortunately your roomates have to buy into this also. That could be harder than training the cat. Good luck!
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Smile, it will make them wonder what you are up to!

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