As for the burning smell, since you did mention that it seemed as if the parking brake was still engaged, it is probably the brakes. If it doesn't release all the way, the brakes will drag, thus giving off the burning smell. Check the brake's next time and if they are hot, there is your problem.
The other gremlin you got sounds like a fuel pump. If it isn't running at the proper PSI, the engine will starve and die out, then catch itself before it completley dies.
These are my two cents from my experience's.
Good luck and Happy New Year.