YOu got it right with the intra city flights, most are used like you described.
AFAIK having two bases in the same metro area is fair game. whatever floats your boat is right in this domain because anyone has the same number of possible bases.
And for your last question, i can't give you a definite answer. It all comes down to how you wish to play. Washington-Dulles is a big airport with a good number of airports around it to fly to. Chicago-Midway tends to be overlooked as it is much smaller than O'Hare, but that means that basing here means you won't have lots of people to compete with.