Chicken Broth

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.

I've been doing my stocks and few broths not.
I'm just not getting that yummy, flavorable taste after cooking. It's usually tastes as a fat water due to the meat.

Maybe I should ask my mum, since her chicken soup is too good :)

Sounds like perhaps you might be using too much water...but it's hard to say as I would need more detail. After it is cooked and cooled are you skimming the fat? Because it should not taste fatty.

Also if you are looking to make a good chicken soup like your mothers then I suggest you watch the lesson on how to Make a Broth Soup as making a chicken soup and making a broth are slightly different (different ratios). You may also want to watch the lesson on How to Make Stock Bases Soups.

Hope this helps - cheers!

I made a big batch of this, but it seems to have soured after less than two weeks in the fridge. How long should I have kept it there? Should I freeze it instead. Why does it sour?

Two weeks is pushing it. After 4-5 days a stock (or soup/stew) should be brought to a simmer to extend its self-life. Moist preparations, even milk, will sour because of a fermentation that occurs, some good, some not so good. Fridges only slow down eventual spoilage, not eliminate it. Make sure to label and date your cooked and stored preparations so you can keep track of them - a must practice in the industry too often neglected by the home cook.

Loving this recipe, came out perfect and it was really tasty too

What about all the leftover mirepoix after the broth is done? Should you discard these vegetables or can they be used?

Just as in making stock, the vegetables/mirepoix should be discarded afterwards as all of their flavor has been extracted by the broth. Cheers!