Jordan pushes with a force of 50N> on a crate. The friction forces are 100N<. Will the crate move? What is the acceleration of the crate?

The crate does not move, and its acceleration is zero. Although it's very convenient to treat the effects of friction as a force, and that process usually describes reality quite well, friction is not a real force, and it can never act like a force that's greater than the net applied force. If it could, then we could set a heavy crate down on sandpaper, and use it to generate electricity while it scoots around in response to the large forces of friction under it.