Yes, Elmer’s will work for this. The process is similar to using Mod Podge—you’ll need to coat the picture with glue and let it sit on the wood overnight, then soak it off with cool water the next day.
Yes, but it's not really worth it since you will be adding shaving cream. The lotion, shaving cream, and foaming hand wash will make the glue look white, instead of...
Elmer's glue is water soluble so the newspaper will lose its shape if it gets wet. Two layers of newspaper will not have enough strength to hold a shape.