1. What does washing the curd typically do for the cheeses?
Removes lactose and leaches calcium out of the curd gel.
The recipe for Gouda involves a lot of stirring, like 40 minutes or more over the whole recipe. What does this stirring do for the cheese and how does it give it characteristic Gouda qualities. Is this for texture or chemistry?
Both. Stirring (agitation of any kind) encourages syneresis. Syneresis creates final moisture in cheese. This moisture level determines rate of reactions during maturation because almost all primary maturation dynamics are a form of hydrolysis.
The Edam recipe involves dropping the pressed wheel back into whey at 50 degrees, is this just to make the curds knit more closely?
Depends on the exact process, but yes, that's the idea.
What difference will there be if I stir the Gouda gently or with some force?
At what point? Force at force will shatter curds. Later on, speeds syneresis.
What effect would adding cream into a cheese recipe have?
When in the process? Milk composition is huge; affects gel strength, rate of syneresis, etc. Can you re-ask more specifically?