a) If the charged particle enters the magnetic field from outside, depending on the width of the magnetic field, the trajectory will be a portion of the circle.
If the particle gets created inside the magnetic field, it will complete a circle provided the width of the magnetic field is sufficient.
b) In a helical path, the velocity component parallel to magnetic field makes it move along it. The circular path will be perpendicular to the magnetic field.
c) Power P=→F.→v=q(→v×→B).→v=0
d) If both →E and →B are present and →E∥→B, path will be helical.
If both →E and →B are present and →E∦→B, radius will not be constant, hence it cannot trace a circular path.