Hi. Are we as the public allowed to sell our paintings to you guys and if so, how does the process go?

Most museums have a private curation process that can be obscure to the public. Typically museums don't buy paintings but accept donations of art, which is tax deductible. Even then, the pieces may not be accepted if they don't align with the museum goals.

There is a vetting process for art. I would call the curator of the museum.

Sorry pretty lady