Can I use tape instead of glue, and can I use origami paper?

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...

You can, it just won't be as flexible when you fold it. I'd recommend not adding stems, as that will put more weight on your flowers.

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...

Yes, you can. You can make it into decorative stickers since Washi tape is a decorative tape.

It can be regular duct tape, as long as it isn't see-through. It should be black, if possible.

Origami paper is thinner than most other paper, and would fold much more easily than writing paper. Gift tissue might work if it's not too soft.

Yes, you can use any paper that is easy to handle (printer paper, construction paper, etc.). But make sure that the paper is a square and has equal sides (unless...