Light fron the sun takes about 8 minutes to reach the Earth, not 4 minutes. I'd think you'd see the sun first, then the house lighting up; when you see the sun itself, light takes a straight (assuming no atmosphere) path from the sun to your eyes, when you see the house, light goes from the sun...
Well, the vertical component of B was given in the problem, so I don't think you need to do the cross product. You're probably just having problems with unit converstions.
Nenad is right, the observers do not agree, but they are both correct. When an observer is accelerating relative to the Earth, he sees the Earth gaining an incredible amount of kinetic energy. However, he is not in an intertial frame of reference during that time. He does not actually have to do...
I didn't bother going through your work, but I got the same answer, 3010.4 N. So I assume it's correct. Also, the distances in your problem were given to 2 significant digits, so realistically the answer is correct to only 2 sig dig.
The speed of light can easily be derived from Maxwell's equations. But I believe in relativity the invariance of the speed of light is considered to be a fundamental postulate, proved only by experiments. If I'm not mistaking, this postulate is more general than what can be derived from...