A charged particle moving in a magnetic field experiences a force toward the top of this screen when it is moving toward the right and the field is into this screen. Is this particle positive, negative or neutral?

Use the right-hand rule to determine the direction of the magnetic force on a positive charge: Point your fingers in the direction of the velocity (right), curl them toward the direction of the magnetic field (into the screen), and your thumb will point in the direction of the force (upward).

Since the force is upward and the right-hand rule applies to positive charges, the particle must be positive.