My hot water faucet will not turn off at the handle. I have replaced the interior stuff and where the handle was not stopping but turning round and round now works....I turned on the valve under the sink and the handle still does not seem to have any influenence on stopping the water. Whats next the shut off valve?

My outside faucet has a little bit larger than pinhole size leak. I have tried repairing it with the "clay like" concoction sold in hardware stores. That worked somewhat but despite the fact that the water is turned off, there still is some tiny bit of water which is coming through and which doesn't seem to allow the "concoction" to harden. It maintains a "putty like" consistency. Any suggestions? Other than calling a plumber. Also, I dug into the soil to see if I could replace that section of the pipe but it appears to be pretty deep and/or is connected directly to the well close by.