Remove any burrs off the end of your stub pipes using the reamer on the end of your pipe cutter. Take a 3/4" double compression fitting and slide one nut and ferrel onto your extension pipe. Tighten down the connection to the center compression coupling.
Repeat the steps for the other stub pipe, sliding on the nut and ferrel. Then, tighten it to the compression creating a watertight seal. Attach the soft tubing to the compression coupling by sliding one end of the tubing into the coupling, then tightening it down at first by hand. Tighten with a wrench while backing off with another.
Use 1/2" copper clips to secure the pipes to the wall. Simply place the clip over the pipe, then screw them in with screws and shields. The LAV stop connects the same way as the water lines. Tighten down the compression fitting to make the seal. Run the hot water line to the left and the cold on the right to match the faucet.
Coat the thread of the male adapter with Teflon paste, then firmly tighten it into the old cleanout threads. Glue in a new Y fitting with a cleanout. On the open end of the Y fitting, run your drain line out to the sink area. Make sure to keep a constant pitch for drainage. Connect the water lines from the faucet to the water pipes.