You can get the white plastic barbed x male pipe thread branch tees at home Depot or Lowe's. They are with the plastic and brass fittings near the copper tubing in the hanging bags. You can also find the barbed tee in a harder grey plastic in the section with irrigation valves, fittings and tubing.
There may also be some small brass barbed talves there to use for the tank drain valve.
The grey push pull valves were typically used as hot and cold low point drain valves. It is a valve with a tee shaped body and not a valve and tee.
Your grey valve is an old style that is no longer made.