Have you got two single faucets or a single lever faucet? It could be a pressure imbalance or it could just need maintenance
The attachments for portable dishwashers are not universal, and do not fit all faucets. To fix this, a person can buy an attachment for their faucet the matches the dishwasher.
Get an adaptor
u may need to tighten it a little or just get a new dishwasher(new!)
Nothing, it should all come with the dishwasher. It fills from the faucet.
Possibly unscrew your aerator at the end of the spout and see if the screen is clogged. Blow it out and rescrew the aerator on. If that isn't the problem, sometimes things get caught in the spout. Unscrew the spout and turn the water on. If there is water coming from there and not out the spout when it is hooked up, the spout is plugged. If no water coming out when the spout is off, rehook spout and change cartridges or stems in the faucet AFTER shutting the water off. Depends on the brand of faucet, check the instructions for the brand and model. Also your kitchen dishwasher and sinks are run on seperate valves. The dishwasher valve is usually under the sinks (causing the water to go to the dishwasher first) the valve that was installed for the sink (before the dishwasher) may be bad too.
In 1966 they had portable dishwasher.Which they would roll to sink, hose snaps onto faucet and it drains into the sink.
Your kitchen faucet is getting bad, the water line that runs to the dishwasher from the branch under the sink has nothing to do with the faucet. the only way the faucet would run is because the gaskets or seats are getting bad. The dishwasher will not affect any water in the house,water goes into the dishwasher and leaves through the drain, it never will reenter the water system,so if you have a white residue,it sounds like you have hard water. If this sediment is inside the washer,you might not be using the right soap for it. Also, the water for the dishwasher should be hooked up to the hot water line not cold.
Because your losing "volume" possibly the piping is under sized or the internal diameter was reduced by mineral deposits
My guess is your garbage disposer was also replaced and they forgot to knock out the plug before connecting the disposer hose/drain It sounds like you have a vacuum breaker on the drain for the dish washer. This is probably just a coincidence but your vacuum breaker needs to be replaced or repaired. It really has nothing to do with the faucet installation.
Not sure what you mean by dishwasher vent hole, but you probably mean the air gap fitting. Some dishwashers connect directly to the disposal, with the tube going up a little to prevent stuff from going back to the dishwasher. But as for removing the air gap fitting, if you have it already, it may depend on where you are. California plumbing code requires a dishwasher air gap fitting above the flood level rim, even if you have a disposer, but I'm not sure if the national code also requires. In any case, if a code requires it, it may be a good idea not to remove the air vent. I would check your local code. You may want to consider a faucet with a built in sprayer instead.
If they are under the kitchen sink, one is for the faucet and one for the dishwasher. Any place else, somebody had a reason at the time probably. Where they are at and the routing of the pipes should give you some idea.
If it's the drain pipe, tilt your machine over and remove it from the pump, clean it out by holding it tight to an outside faucet. -You now need to check the strainer/filter in the floor of the machine, it may be broken.