If mass (consisting of protons and electrons) can be converted to energy by running it at the speed of light, wouldn't that also convert charge as charge is due to and quantized over electrons?
For instance: I take a system with two pens and transfer 100C charge from one to another, then run the -ve charged pen at speed of light so it is mostly energy. What happens to excess electrons?
Mass is not "converted to energy by running it at the speed of light."
Mass is converted to energy in situations like radioactive decay, where the total rest mass of particles produced is less than the total rest mass of the initial particle, and the missing mass is converted to kinetic energy of the remaining particles (total kinetic energy=[initial particle mass-total final particle mass]$c^2$).
But when something is moved near the speed of light, its mass is not "converted to energy." Rather, that thing just has more energy than it had when it was standing still ($E>m_0c^2$, where $m_0$ is the rest mass). It has the same rest-mass energy plus kinetic energy that it got from something else - from whatever did the work to speed it up, not from its own mass!
As John Rennie pointed out, here's a stack exchange question where it is proven that charge is conserved, even when things are moving near the speed of light. So just like with rest mass, moving something at the speed of light does not somehow "convert its charge to energy."
Speculating a bit - it seems like your understanding would be improved by working with a few examples of keeping track of energy in radioactive decays (look at example 2 on this page). It seems like the central problem is that your understanding of relativity is based on hand-wavy english sentences like "mass can be converted to energy" (true, but not in the way you understood it) rather than equations with specific and clear meaning.
