When they flick their tongue out, they're just smelling. They smell by putting the tips of their tongues into two spots in the top of their mouth that acts like our nose. They flick their tongues when they're exploring. And the staring is just a thing they do sometimes. Our female does it a lot. She'll just stop exploring and stare at me for a minute then randomly start exploring again. I've started making faces at her when she does it haha

Not sure of any ways to keep them from biting, just try not to handle them right before and after sheds and if she looks grumpy just leave her be for a day or so.

You don't necessarily have to feed her in a separate tub. We feed both our ball pythons in the tank and they don't have any cage aggression.

Just talk to your mom. The best thing to do is educate her with knowledge about ball pythons rather than just the misconceptions she has about snakes in general.