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  1. Now what exactly happens when magnetic field and electric field is applied perpendicularly? What happens when they are not perpendicular?

  2. In the question, it says that a magnetic field and electric field is applied. So why are they taking B to be into the page and E radially outwards? Is that arbitrary or is there some particular reason?

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The force on a moving particle in a magnetic field is always perpendicular to the magnetic field and the velocity of the particle. These three vectors are not in a single 2D plane. To draw the situation on a sheet of paper, the arbitrary choice was made to choose the plane of the circular trajectory of the particle in the magnetic field for the plane of the paper. To cancel the force from the magnetic field, the direction of the force from the electric field must be opposite to the force of the magnetic field and of the same absolute value. This fixes both direction and value of the electric field.

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