What kind of glue can I use to cover the cracks?

PowerPoint isn't a good tool to use if you really want a professional-looking cover. If you're doing it yourself, you need a real image manipulation program (Gimp is free) and...

You usually only need one or the other. Really it's whatever you like. I personally like primer better, but it is up to you. Try both and see which one...

A good quality regular super glue, or better yet, a gel glue like Loc-Tite. Tiger glue is also good quality.

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...

You can use clear glue, or any type of liquid craft glue. If you use a glue stick you will have to microwave it.

Use a good glue stick as that won't seep through the page and ruin your drawing (it doesn't wet the page like liquid).

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.

Tape will not last as long as glue, especially a glue made for paper. There's no reason you can't use origami paper, though.

You shouldn't need to. If a board itself is cracked, you may just want to replace that board.