When using the erasure or erasure background tools, it leaves a checkered background. How can I get the erasure tool to leave a white or color backround?
The checkerboard means the area is transparent. If you save it in a format that doesn't allow transparency, like jpg, it will turn white. Alternately, set your background color to white or the color you want and use the regular eraser on a background layer.
Jpegs can't have transparent areas. Most likely you had layers and were forced to save "as a copy", which means that the image which remains open in PSE is not the jpg. A file saved as a copy makes a copy in the save format, but it's not like save as where you now see the newly saved version instead of the original. The original remains open and unsaved onscreen.