I didnt quite get what you elaborated...

a) I meant Z_F0 is free space impedance 377 ohms. If you have the E-field given, then also H-field ist given via Z_F0

b) U use a formular for static fields. But as far as I see we have a constant frequency continuous wave travelling in free space. Since its sin-wave we have to get average rms value that is expressed with 1/2

c) Definition of poynting vector is: S = E x H whereas all components are 3d vectors.