Questions About Stars

I would like to know if you can tell me if this is Capella. Looking through binoculars, it changes shapes. It looked like a flower with bright red on the end, yellowish in the middle and green on the end.

Changes in the color and shape of an astronomical object are optical effects rather than real changes in the object.  The ring-shaped patterns could be caused by an improper focus.  The color gradient from red to green is due to chromatic aberration, which causes different colors of lights to focus at different distances behind a lens (here is an image).

Can you tell me if Betelgeuse will move all over the sky or will it move in it's immediate area?

It isn't entirely clear what you mean.  Betelgeuse will appear to move across the sky over the course of a night due to the Earth's rotation, as will all stars, but it will remain fixed relative to other stars.