Yes, voltage is related to the kinetic energy of each electron. An electron moving through a potential difference of 100 volts gains twice as much kinetic energy as an electron moving through a potential difference of 50 volts.
Current, however, is not related to speed. You can have a large number of very slow electrons passing some point in a wire, or a smaller number of very fast electrons, and the current will be the same. Keep in mind that the actual speed of electrons in wires -- the speed they move from one terminal of a battery to another, for example -- is quite slow. You should not worry much (at this point) about speed at all.
Resistance is not so much a process of slowing electrons down as it is a process of stripping them of kinetic energy and turning that energy into heat. Certainly, you can't reduce kinetic energy without reducing speed, but it's much simpler to view resistance as a phenomenon of energy rather than speed.
- Warren