It is not recommended to use bleach or drain cleaner in garbage disposals. the chemicals can cause corrosion and can splash up, causing damage to counter areas and nearby persons. It is best to follow your disposal's instructions for cleaning and remove and clear the j-trap of the sink instead.
yes
The sink drain is blocked somewhere after the disposal. take apart and clean or renew sink drain.
As long as the drain basket for the disposal will fit the drain hole in the sink, there shouldn't be a problem
garbage disposal
It possibly has garbage trapped in parts of it or the tube right below. Fill the sink with hot water and drain it through.
physical change
The only issue would be the drain hole. I couldn't find a measurement of what it is. I would imagine a new sink would have a standard size hole. I do not know about an older one. I have never seen a smaller drain for a garbage disposal but that doesn't mean they are not available.
To keep your sink clean and clog-free, a cheap alternative to expensive products is to pour boiling water down your sink every few days. If your sink is clogged, try a solution of baking soda, and a few tablespoons of vinegar before rushing out to buy expensive drain cleaners.
The appliance under the kitchen sink that grinds food waste and puts it down the drain.
If you have a stink coming up from the overflow drain in your bathroom sink, you have some garbage down there that you should not have. You probably have a lot of hair clogging the drain. It is probably slow draining. You need to clean it out and get rid of the gunk.
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.
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.