Unless there is another issue like drain location or cabinet design it is pretty much personal preference. The side closest to the dishwasher if you have one would probably be best for the dishwasher drain hook up
yes
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.
Yes. Your dishwasher discharge hose is probably hooked into the side of the disposal. Running your disposal will not hurt the dishwasher.
Either side that you want. Most would probably put it in the smaller side.
If it is a double sink, does the other side drain? Are you trying to fix the disposal because it does not come on or because it comes on but does not drain. If it comes on but does not drain and the other side does, it is probably just clogged with food. They make drain cleaners for disposals. If neither side drains, put the stopper in the disposal side, hold down on it and plunge the other side.
This will only happen if the drain pipe is clogged further down the line, near or in the wall. Possibly if the garbage disposal has been installed by an amateur, the 90 fitting going to the other tub has been installed the wrong way.
Most common is a center drain, but it can be at either side depending on where the drain goes into the wall. On the side closest to the dishwasher, the tail piece directly under the sink has a smaller tube in the side of it for the dishwasher drain.
If the sink/sink drain fitting connection, sink drain fitting/disposal connection, dishwasher/disposal connection, disposal/drain elbow connection are what are leaking they can either be tightened or have gaskets replaced or other sealing methods used. If the disposal is leaking elsewhere the disposal needs replacement.
If the tubing between dish washer and garbage disposal unit is newly installed then someone forgot to remove a plug. If it was working before then the flow from dishwasher to the garbage disposal is too slow resulting in this.
The sink doesn't have an adequate vent.
On the side of the disposal, there is a tube, 1/2 inch diameter and 1 1/2 inches long. This is for the discharge line from a dishwasher. The knock out plug in in that tube. If you do not have a dishwasher, you leave the plug in so that the disposal will not leak. Having the dishwasher empty into the disposal helps keep it clean and free of food particles.
As a very expensive garbage disposal. Anything you throw at it (i.e. toxic waste, nuclear waste, etc.) with be disposed of without side effects to the environment.