How to remove old facuet?
To remove the faucet (looking at the center photo) there is a brass hex nut (just above the braided plastic hose connector) that is tightened to hold the "C" shaped spacer and the faucet securely to the sink basin. You can use a Basin wrench (it has a swiveling head on a long handle) or an adjustable crescent wrench with a short  handle. Either way loosening the nut will enable the faucet to be removed from the sink. You will also want to shut the water supply off on the hot and cold lines first.