We made a vessel sink from a copper bowl by cutting a hole in the center and installing it with a pop-up drain. The sink does not have a lip around the hole like the other vessel sinks we've seen. Water stays in the bottom and it doen't drain completely. How can we get the last 1/4 inch to drain?
You will need to peen a recess in the bottom so the top of the pop up will be lower than the bowl. I have never done it myself, but as a welder I can make this suggestion.
Copper is a rather soft and easy mailable metal. If you take a block of wood and create a negative image into the wood then the bowl can be set over this so you can peen the center down. You will however want to use a hard wood like oak, or hickory. I would use a piece about 4" x 4" as this will allow enough to sit the bowl onto. Also you may want to use a wooden hammer. That is, the face of the hammer is made of wood. This will take quite some time and may want to practice on a scrap piece of copper to start with.
Nope, copper is very malleable and shouldn't need heating. It will probably take hundreds of hits, so work slow and deliberately and don't expect immediate results. It will take a lot of forming to stretch that metal out.