What factors limit the speed of voyager 1 and similar rockets? Are there equations that sum it up?
Yes. There are a lot of equations, but that doesn't depend upon fuel. Rocket equation is the same (independent of fuel). The volume of fuel exhausted at the nozzle may change (difference in density of fuel, rate of emission at nozzle, etc.). This may result in a different value but AFAIK, the rocket equation remains the same. I don't know much about their fuel. But, you can check it out at Wiki for both solid and liquid propellant disadvantages.
Radioactive fuels are already in use. Nuclear rockets use a reactor to pump hot gases out. Looks like they're much better than chemical rockets.
What would be required to accelerate a rocket to relativistic speeds, and how practical it is?
No known fuel exists for that kind of question. But, we know that antimatter can be used for such Relativistic velocities. Still, it is theoretical. Maybe something would arise in the far future. But, not now..!