You are right, on your three points, about Elvis Presley, except for one thing:
He was NOT a great guitarist. The guitar was a stage prop. He had a session man, in his band, who played the real guitar parts.
Elvis had a wonderful, sexy voice; he was a crooner. He said that his singing idol was Dean Martin. I remember his first appearances, on the Ed Sullivan show and in his very early movies. He was mesmerizing.
It's fun to parody him, but we should also remember the contribution he made to our popular music.