First of all, I'd like to say that I'm not an extremely handy person and some of the plumbing jargon used may confuse me
Basically, this starts after we run our dishwasher (which is one of the rolling models that you have to manually attach and remove the line to the faucet)..everytime I attach it and turn the hot water on, you can hear the pipes banging in the basement (maybe the dishwasher is causing excess pressure to the faucet/sink fixture?)...when it completes it's cycle and I detach it from the faucet, it will still be dripping...later on when we turn the faucet on and off, it'll either continue to drip or worsen into full out pouring
Been living in this house and using the same dishwasher for a good couple of years now and only started having this problem about 9 months ago and I'd like to say that replacing the dishwasher isn't an option (manually washing dishes is out of the question also (far too lazy ))
Your dishwasher uses a solenoid valve to allow water to enter the unit. This solenoid valve operates very fast and is causing water hammer. Install a couple of water hammer arrestors on the system somewhere, one for hot and one for cold.These are like shock absorbers for the plumbing system. Yu can get them at most hardware stores for about $12 a piece.
Your dripping faucet is another issue depending on the type. If it has 2 handles, its a matter of replacing the worn washers with a couple of new ones.Though you must use the correct ones and you wont know this until you pull it apart.
If its a single lever faucet, the cartridge must be replaced. Some brands offer free lifetime replacement cartridges, some you have to buy.
Moen is one of the brands with free replacement. Your local Home Depot stocks these and will give you one for free if you take in the old one.