My truck had this problem. The headlight switch was shorted out in such a way that the dash lights would not come on, and the over head light would not go off. I also have a bad ground somewhere...
yes you can
I would say the 2001 would win if it was 5.7 vs 5.3 because the newer 5.3 i believe has more horsepower. but it would depend on gearing.
Never heard of a 350 big block Chevy. There was a 348, discontinued around 1963, and a 366, which was only used in larger trucks.
check you brake fluid level.