Rouxbe

When I take the chicken out, I let it cool just long enough for me to be able to strip the bird, then I put the carcass back in the pot and simmer all night. An hour and a half broth seems like it'd be rather thin.

Putting the carcass back into the broth is a good idea Joel. For other recipes where you might like to darken the broth, you could even roast the bones for 30 to 45 minutes to obtain some carmelization (brown color). Adding this back to your broth would yield a dark chicken broth.

However, there is a point in stock/broth making where you can no longer extract any further flavor from bones and mirepoix. You can simmer it overnight but you will only be increasing the flavor through reduction (and not extraction). In other words, you could strain after a couple of hours, then reduce to increase the flavor and you'd obtain the exact same results from cooking it all together overnight. The only danger in cooking overnight is that the vegetables may break down to the point where they actually start to cloud your broth/stock. Hope this makes sense.

Best and safer to simmer in a dutch oven in a low oven if you're going to do this overnight. Do it in a 250 F oven, with a lid slightly ajar, to prevent evaporation, and create the gentlest simmer possible (if fat, it will barely poach). This should result in a cloudless, very flavourful stock.

If you think using a whole chicken would cost a bit too much, you can use just thighs and legs. It won't taste quite the same but it'll be near enough.

Remember though, that you often make broths when you are going to use the meat off the bone in the final dish that the broth was made for. So you are not going to throw away or discard the meat.
You are right though, making broths with legs and thighs is a great idea.

Can a chicken broth and chicken stock be used interchangeably? Or does a stock give a better flavour due to longer simmering?

A broth is typically used when the whole meat used to make the broth, is re-incorporated back into the broth. See the Chicken Pot Pie recipe for an example.

Both will have good flavor. Some will argue that the stock may have a bit stronger flavor given the longer cooking times.