Always use cold water when operating the disposer to solidify fatty & greasy waste so they will be chopped up & flushed down the drain. From The Friendly Plumber.com
Yes if you do not you could break your garbage disposal.
no
turn it on
Yes the outlet for the dishwasher should be on the same side as the disposal,so the disposal can handle the waste water from the dishwasher.
Your source of water should not be an issue. But it may be an issue if you are on a home septic system. Some say not to use a garbage disposal when you are on a septic system, but you can. I know of some in use with septic systems and they have not had a problem. Generally you should have your tank pumped every five years. With a garbage disposal on the system you should have your tank pump every two or three years,
You should be able to as long as you use enough water both while using the disposal and after to make sure it all goes down the drain. While zucchini skin is tough, it doesn't have fibers or strands that could bind up on the cutting knives in the disposal.
Both
Defective garbage disposal.
run cold water thru it for a minuint after you are done with it, cold water should be running while you use it also,
The water assists in chopping up the items being chopped and washes them down the drain to prevent stoppage.
Put ice cubes in disposal and run water as usual until ice cubes are shredded.
It possibly has garbage trapped in parts of it or the tube right below. Fill the sink with hot water and drain it through.