Making caramel: how the ingredients effect the outcome?
Here's the function of each ingredient, as I understand them:


Sugar - Obviously, this is the thing that caramelizes.  You need it.  The amount of sugar determines the amount of caramel.
Water - The water helps early in the cooking process by causing the mixture to heat evenly without burning.  Most of it boils off.  As the water evaporates, the boiling point of the mixture increases.  So, you can determine the ratio of water to sugar by measuring the temperature while it's boiling.  Once enough water has boiled off to reach the temperature specified in the recipe, then you know that the ratio of water to sugar is right.  Too much water and the caramel will be too soft.  If you add extra water, it will take longer to reach the target temperature, but you'll still have the same amount in the end as long as you get it to the right temperature.
Lemon - A bit of acid helps the caramelization to occur faster and at a lower temperature.  This can be useful if you want a soft caramel because you won't have to boil off as much water.  It can also reduce the risk of burning because you don't have to get the caramel quite as hot.
Salt - This is just for flavor.  In the small quantity normally found in caramel, I wouldn't expect it to make a difference to the cooking time, target temperature, or texture.


A longer cooking time allows more water to boil off, resulting in a harder (or possibly burnt) caramel.  Otherwise, it doesn't affect the outcome that much, unless you're making a low temperature caramel.  There are some dulce de leche recipes, for example, that require cooking for 13 hours.  At higher temperatures, the reactions happen a lot faster.  At 350 F, for example, the caramelization happens so quickly that there's no need to hold it at that temperature for any significant time.