Welcome to Just Answer, I will do my best to help with your problem

Go ahead and post your picture

It's called a stem

But that's not going to get you the part on any site

You need the brand of the valve at least

then you might find it on a specialty part site

Check this site out. I't probably your only shot at finding it. but if you don't know what you have it's a needle in a hay stack

http://www.chicagofaucetshoppe.com/

you need the brand of the valve/faucet

Taiwan is where it may have been made

if it is Taiwan then you're out of luck. Nobody will have the part

You're only shot is if it's a major American manufacturer

replacing the whole valve/faucet may be your only option

Yes, you just connect the existing piping to the new valve. 1 handle pressure balancing valve is all we can use now in the States

Yes, is a code requirement to prevent scalding in the shower

Any new valve no mater the number of handles has a hot and cold water line into the valve. It may just take a couple more elbows to connect a 1 handle valve

You're welcome

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