Sauron still has a physical form during the events of LOTR. Frodo sees him through the tower window when walking towards Mount Doom, and Gollum remarks he was personally tortured by him, and that his hand has 4 fingers.
Dwarves seem resistant to the rings because of their mechanical nature. As you described, they were first designed by Aule instead of Eru, and then given free will, so that gives them a more “automaton” nature than the other free peoples