IB Physics Where do Magnetic Fields Come From?

A tutorial sheet of questions, from SL, HL and the Relativity topic is given below.

S is a reference frame at rest relative to the laboratory. S' is another reference frame moving at a constant non-zero velocity relative to S.

1. An electron is at rest in S. Is there an electric field in S? Is there a magnetic field in S?
2. An electron is at rest in S'. Is there an electric field in S'? Is there a magnetic field in S'?
3. An electron is at rest in S. Is there an electric field in S'? Is there a magnetic field in S'?
4. A uniform magnetic field B acts along the X axis in S. There is no electric field in S. S' moves parallel to the X axis of S. Is there an electric field in S'? Is there a magnetic field in S'?
5. A uniform magnetic field B acts along the X axis in S. There is no electric field in S. S' moves parallel to the Y axis of S. Is there an electric field in S'? Is there a magnetic field in S'?
6. A uniform electric field E acts along the X axis in S. There is no magnetic field in S. S' moves parallel to the X axis of S. Is there an electric field in S'? Is there a magnetic field in S'?
7. A uniform electric field E acts along the X axis in S. There is no magnetic field in S. S' moves parallel to the Y axis of S. Is there an electric field in S'? Is there a magnetic field in S'?
8. Two electrons each move at a constant velocity v along parallel paths. In S' the electrons are always on the Y axis at a distance d apart. (a) what are the forces between the electrons in S? (b) what are the forces between the electrons in S'? (c) is the magnitude of the force between the electrons the same in each reference frame?