Brass Rough-In Posi-Temp Pressure-Balancing Cycling Tub and Shower Valve - 1/2 in. CC Connection

Yes, that's exactly how I installed mine. You'll have to close off the bottom outlet with a capped off pipe, then plumb the upper one to the showerhead.

I would really check with a plumber. We installed it with a tub/shower, and frankly it's been quite a while and I can't remember if it could be either/or. You might also check the Moen website-I went there for a lot of my information. Sorry I can't be more helpful.

I believe this cartridge supplies both hot and cold depending on the position of the handle. The balancing cycle eliminate the valve from going all hot when a faucet or toilet is opened on the same plumbing run.

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CC is a fitting that you solder. IPS is a threaded connection. Not clear why Home Depot, who's all about homeowner DIY projects, uses such confusing language. CC means confuse the customer. You will have to decide which type you want to use.

This valve is designed to be used with a tub/shower combination as the flow is diverted up when the lower (tub flow) is blocked at the spout. You could plumb the lower flow to the shower head and then add a valve in that line to block the flow allowing the upper flow to divert to the overhead shower. The flow to the overhead shower would probable be just on/off. Also you would want to review the installation guide for this valve for minimum/maximum distances restrictions. Keep in mind that since other valves are available that are specifically designed to accomplish this you may wish to consult with one of the in-store plumbing associates before you commit to this arrangement. Hope I helped.

This is not a pressure regulator, this is a shower mixing valve. This valve is installed in a shower to control water temperature.

This part really doesn't have anything to do with whatever shower head you want to use. It's the actual trim kit (I have #T4502NHBN) and pipe size you have. Also, be aware that you need to have the pipes behind the wall at an adequate distance for the handle to sit correctly (if this piece is installed too closely to the wall, chances are your handle will stick out about an inch too far...see image). Unfortunately, I don't recall the correct distance that pipes should be for clean installation (mine sticks out too far and couldn't be corrected by the time we realized). I hope this helps?

I'm not a Home Depot employee but I don't believe they carry any in-store combination shower controls. Why would they have so many options and not have one that you can control both the temperature and the volume of water separately? They are made but HD doesn't carry any.

A pair of vice grip pliers will do. Just make sure to hold the valve securely as not to cause damage to the piping. Steady, constant pulling pressure will work better than quick pulls.