These are questions your painter should answer. I'd suggest a different painter.

A search here on Houzz should give you many, many options for what paint, and the color is up to you.

Hi, at Settings Interiors we prefer having our custom built-ins sprayed in Lacquer rather than paint. Avoid a high gloss finish and go for a satin or a semi-gloss. Some of our favorite whites are "Delicate White" by Pittsburgh paint and "Snowbound" by Sherwin Williams. It's also a good idea to look at your existing trim color before you introduce a different shade of white. Best of luck with your project!

We always suggest oil-based paint for wood furniture and cabinetry, as it is much more durable and the finished look is superior to latex paint. To pick the right white, it is important to look at the colors of the walls around the built-in, as white shades bring out the undertones in the other colors. You may want to try a few different white sample boards up against the surrounding walls to get the best idea of the shade you should select.