In answer to my own question about a Muggle doing magic-
On page 64, fourth paragraph, Ted Tonks tells Harry, “...Anything else broken? I’ve fixed your ribs, your tooth, and your arm, I’m Ted by the way-Ted Tonks, Dora’s Father.”
Since Harry’s tooth had been knocked out, I am assuming that Ted Tonks did magic.
Ted was a Muggle born wizard.