The earth orbits the center of the galaxy once every 225 to 250 million years. Presumably the black hole at the center rotates much faster and spiral arms further out go somewhat slower.
We've been observing galactic rotation for about 90 years. I'm not sure we have enough data to say for sure how fast any galaxy rotates. But ask me again in about 30 million years. :o)
Everything in a spiral galaxy rotates around the center of the galaxy at the same rate. It’s as if every disk-like galaxy were a giant phonograph record, everything rotating in lock-step. It’s one of the great discoveries in astronomy, made by Vera Rubin. She probably should’ve gotten the Nobel Prize for it, but never did. She made it by studying stellar red shifts (fortunately, they don’t have to watch the galaxy rotating for tens of millions of years before getting a fix on the rotation rate!)