My outside faucet's shut off valve is turn off, as well as the outside faucet itself but the hose is still dripping quite A LOT, and you can hear the water running in the pipes in the wall. Can I fix this? Thank you for your time.

The outside leak can be fixed by getting a hose bib with a shut off, attach this to the faucet and turn off the valve. The water running in the walls could be serious. Try to shut all the water off in the house and then listen to hear if it still is running . If you still hear the noise best get a plummer to come out.

Do you know if this is a frost proof spigot or not? From inside your basement can you describ how thius line connects to your inside plumbing?