I have two questions about electromagnetism that I would like to ask. The 1st one is as follows:

I have two point charged particles A and B a distance x apart. A and B exert a force on each other by Coulomb's Law, but a force is exerted on the particles to keep them apart at exactly x distance, thus making the system remain in equilibrium.

If the particles are in a stationary inertial frame, then there is nothing wrong. However, consider the case where A and B are in an inertial frame moving at constant velocity, and we are viewing the particles at a rest frame. In that case, A and B will produce magnetic fields, and these magnetic fields will also affect each other. If they have like charges, they will move towards each other. If they have unlike charges, they will repel charges. However, if we were to analyse the motion of A and B in the moving inertial frame, then A and B will be stationary and there will be no magnetic field. So A and B will be stationary.

How can I get 2 different answers by just taking a different inertial frame? Shouldn't all inertial frames give me the same answer?

The 2nd question is:

Consider the case where where I have 2 charged point particles. A is at the origin (0, 0) moving in the x-direciton, while B is at (0, a), where a is some arbitrary value. B is moving in the y-direction. We ignore analysis of electric fields. Since A is directly on the line on which B is travelling, A will not experience any magnetic field and thus will move straight. However, B will experience a magnetic field by the moving A. How do you explain these by using Newton's Third Law or something? Why don't the forces balance out?

I got quite confused here :S. Do I have some misconception somewhere?

Thanks in advance.