I'm going to use the acceleration of the
fastest car I could find.
(10.9530081301 m/s/s)
It weighs 1,888kg.
It would take 10 months to reach the speed of light with that car's acceleration.
The calculations below are not affected by the rate of acceleration, however remember how strong 11m/s/s acceleration feels to a human.
No it's not. It would require an infinite amount of energy to get an object to travel that fast.
No it doesn't, but it's a very large amount.
It would take 20679 NT of force for that acceleration. Extended over 10 months and 3.8853103e+15 meters, that's 8.0344332e+19 joules. That's equivalent to:
618033323077 gallons of gasoline
2510760375 tons of coal
All these calculations exclude weight of fuel (which involves calculus because it will be used up for the duration of the trip) and the actual weight of the space vehicle.