Well it was a joke, not a solid theory so take it with a grain of salt. But basically yes, it would mean that a single electron is moving around and bashing with itself (although most collisions are done with protons which have a much larger mass). If it can move back and forth in time you can have a gazillion of them at any single moment without knowing they originate from a single source. As for the speed of light, quantum entanglement suggests that the barrier is violated. If there is information exchanged in quantum entanglement, experiments have shown that this information should travel at speeds x100 the speed of light. It’s one of the dozens enigmas of quantum physics. If you have a single electron the enigma is solved.
I don't remember the source but once I've heard a hypothesis that God is an electron with intelligence. It could be the same electron Feynman was talking about :)
I'm not very knowledgeable about this, but I thought quantum entanglement didn't allow for FTL communication? A lot of times the way quantum entanglement is explained makes it sound magical but here's a non-magical scenario with no fancy terms (like quantum superposition, qubits, or wave collapse):
Imagine you create two entangled particles, A and B. They have a number of properties, like momentum, position, and spin. Let's use spin for this example. You don't know these values yet, since they've never been measured—they could have clockwise or counterclockwise spin. However, you know the particles have opposite values. One is clockwise and the other must be counterclockwise. You then allow them to travel really far from each other, and you measure the spin of particle A—let's say it's clockwise. Because of that, you now know that particle B must have counterclockwise spin. You just learned something about a distant particle instantaneously. However, the data didn't really travel anywhere. If you interact with particle A, and change its spin to counterclockwise, particle B won't be affected. So you can't manipulate one particle to have effects on the other instantaneously (or faster than the speed of light).
This explanation seems pretty intuitive to me, but correct me if it's wrong.
EDIT: It almost seems stupid that there would be a whole theory based around this, since one would think we can just say particle A was clockwise and particle B was counterclockwise the whole time, but there is an important distinction to be made. We can't just assume they were in a certain state before we measured them. The whole premise of quantum superposition is that before being measured, the particles are a "superposition" of both states—for all we know they could both be either clockwise or counterclockwise. Just because we then measure them and determine what they are doesn't mean they had a single state before they were measured—that's an assumption. Removing the assumption creates so many consequences that we now have a whole subfield of science dedicated to understanding this stuff.
So back to the particles, if they're in both states before one of them is measured, and now they both have to resolve to one state, in some sense there is something traveling between them, letting the other one know what it has to be.
I don't remember the source but once I've heard a hypothesis that God is an electron with intelligence. It could be the same electron Feynman was talking about :)