Your probably right about why she wants to bring down Shield. Except once again character wise and story wise we don't see it written that way. All we know she just wants to bring down Shield. Possibly just for chaos and entertainment value. Not for a good reason. Again proving the point about fans saying the character has no complexity or development.
Doubtful. Marvel keeps wanting to play the humans hate mutant race card all the time. Even when mutants save the world they still can't get a break.
True yet it could also be because the writers make it so imo.