Does Prime remove copper in the water? Because I might need to use warm tap water for w/c.

The short answer is no.
The long answer is yes and no.

These products work by combining.

Those bonds will be broken down later.

What they are hoping is that by the time the bonds are broken down, your aquarium or filtration will have ab/adsorded it.

You would need a 5ppm level of copper to even notice it. If you've been using hot water for anything, I seriously doubt if you would have levels even a fraction of that.

I was told all the hot water going through all the copper tube/hose before reaching to our facet.

That it does

The green color you see on the inside of copper plumbing is oxidation.
Like rust, it seals it off.

If it didn't, your plumbing would dissolve and disappear.

Like mine, lol. There is a leaking pipe in our laundry wall and it's going to cost a fortune to fix. Good info on copper, thanks.

Your copper pipes in your house will self-passivate - or cover their own surfaces with a patina that seals off the fresh copper from entering the water system as the water flows through the pipes. If you have copper pipes in your house that are older than a few months, you should have no worries.

A 5ppm dose of copper would pretty well sterilize your tank - fish, plants, etc.

Because of it's lethal qualities, copper can be an effective treatment for many prolbems in a tank - but the main problem is that the same copper that kills a parasite will kill a fish if done in a dose that is not right for the particular fish. Each fish - size, age, immunity level and stress level - cn vary in it's tolerance for copper. Copper is a nasty thing to have in a tank.

That said, if you are using copper treatments, you can also get copper removers or change out the water. The amount you get from copper pipes in your house is miniscule and not of concern.