Can museums sell their art pieces?

Yes, to collect fund. Only if there are replica available. Its dangerous to sell unique parts of history to private collector who don't know how to preserve or care for.

Yes . . . . I have friends and family who made donations of art, furniture, autos, collectibles etc to museums - only to see them sold and the money frittered-away on high salaries, perks and benefits for the higher-ups.  If you ever donate anything have a lawyer document that the items are to be held by the museum permanently or returned to you or your estate.

Museums sell donated items for cash on the basis of "duplications" in their collection or "new directions" of their collections.  Like everything else, it's a racket - and tax-free at that !!!!!!!