Does an object moving in the y direction have KE? If so if you apply a force in the Y direction will the velocity increase?

Answer 1

The kinetic energy of an object is 1/2*m*v^2, so an object moving in the y direction will have a speed, and therefore also kinetic energy (KE)

If you apply a force in the Y direction the velocity will not necessarily increase, only if the object experiences a net force. For example, if you apply a force in the Y direction on a chair by sitting on the chair, the chair will not move at all.