Your typical coal fired power plant has a thermodynamic efficiency of about 80%. Your typical gasoline powered car has a thermodynamic efficiency of about 30%.
Of course, the electric car has to deal with transmission losses and charging resistance. So overall thermodynamic efficiency winds up being, more or less, a wash.
The real question is, what costs less. At $3.00 a gallon, an efficient car has a fuel cost of 10 cents a mile. A modern electric costs about 5 cents a mile for electricity. Of course, fuel cost is only one consideration.
Most people would keep their gas car for out of town trips and have the electric car for tooling around the city limits. Its more likely to be more of an errands vehicle than a commuter one.
No, it doesn't. According to DOE, typical efficiency of the average coal-fired power plant is around 32%, with the average of the top 10% of plants reaching 37% efficiency.
However, I don't see where you account for the source of the power for the electric motor. Is it magic that fills the battery, or fossil or nuclear fuel?