The disposal is clogged or that side of the sink is.
Probably not, depends on where the clog is at and how the dishwasher drain is connected. I wouldn't chance it, but the worst that will happen is the sink will fill with the water from the dishwasher.
The pump in the dishwasher should keep the water from getting into it.
call roto rooter the pluming specialist they fix it right
The sink drain is plugged,or you have the dishwasher hose hooked up in wrong place.
Partially clogged drain line.
If you don't have a disposal, you can get a Tail piece, the section of drain right below the bottom of the sink that has a Y on it that is the size of the drain from the dishwasher.
Normally you will install a dishwasher drain pipe above your kitchen sink drain, so you are using the sinks P-Trap. When installed in this fashion, no you don't require a seperate. If you want to install your drain elsewhere, than yes you need a trap otherwise you will have sewer gases backing up through your dishwasher and into your kitfchen
Yes, the air vent (air gap) is very much required!! It prevents water from traveling from the sink drain pipe or garbage disposal and into the dishwasher.
The sink drain is blocked somewhere after the disposal. take apart and clean or renew sink drain.
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.
The sound is the dishwasher draining into the sink drain. It is a normal sound.
Unclog drain that both sinks drain into.