Ring size

Oh yes. There's a flashback scene where Gandalf was doing research, and was reading Isildor's account of what the One Ring was like when he first acquired it from Sauron, and you see a shot of it shrinking to fit his fingers, showing the Ring could absolutely change to fit the fingers of the person who had it. In fact, that scene demonstrated that Sauron was apparently a giant in that form before Isildor destroyed that particular incarnation of him.

Fun trivia: for many scenes, they used a prop ring for the different characters to hold or handle; but for up-close scenes, particularly the one where Bilbo dropped it on the floor, and it didn't bounce, they used a very large, heavily weighted prop ring. I think CGI rings were also used, such as when there was a tussle at the Prancing Pony and Frodo manages to catch it perfectly in midair on his finger (which would have been very difficult to film perfectly with a real ring); or when Gollum falls into the volcano 2 movies later and it melts.