There has been a humming or vibration noise coming from my rear right tire area when I approach speeds above about 35 mph and higher. Also, just recently my steering wheel has begun shaking when I travel up to speeds of about 50 mph or so. Any thoughts on what is wrong?

Tire problems would be my first guess. The wah-wah-wah-wah or wup-wup-wup-wup while driving is classic tire noise coming from the rear and that noise manifests itself into shake when the tire is on the front. Also look for out-of-round front rims. Depending on the size of the wheels, a little ou-of-round can feel like a big problem.

Swap your left front and left rear tires (as long as they're not staggered) and see what happens. See if the shimmy goes away.