From your description, it certainly sounds like there is a leak, possibly there is one in addition to the leaking sink faucet. If the pressure tank bladder is damaged, then your pressure tank will not hold the appropriate amount of water, and you would get the symptoms you described. A pressure tank is typically rated for total size in gallons, and how many available gallons of water the tank provides. For example, my well pressure tank is 50 gallons, with 15 gallons of available capacity. This means that if I am taking a shower at 2.5 gpm, the tank should in theory hold 6 minutes of water for a 20 psi drawdown on my pump. This is pretty typical.
Since you describe a situation where the pressure goes down rapidly when there is no water use, it certainly sounds like there is more than one leak, and I would test the pressure tank to see if it holds air. This can be done by measuring the pressure at the valve with a gage to see if it holds when no water is in use. If the pressure fails to hold, you have a damaged bladder.
Since you describe a situation where the pressure goes down rapidly when there is no water use, it certainly sounds like there is more than one leak, and I would test the pressure tank to see if it holds air. This can be done by measuring the pressure at the valve with a gage to see if it holds when no water is in use. If the pressure fails to hold, you have a damaged bladder.