First, everything you see was indeed folded by me. I include the name of the designers out of respect.
The snapology and modular pieces were all done from multiple pieces of paper held together by friction locks and nothing else. Similar for the two dollar bill pieces. The flowers, tessellations, and arthropods were folded from one piece of paper each.
The snapology is really boring to do, and to my mind is barely origami. Its all done from strips, I could teach it in about a minute.
The dollar bill things were made from, well, dollar bills. Believe it or not dollar bills are one of the best folding papers imaginable. If I could easily get the stuff without the printing I'd fold with little else.
The modular pieces were mostly made of Kami, standard Japanese folding paper, one side colored and one side white. Some of the stars also had foil paper, which is thin metallic foil laminated to paper. The floral pieces were made from patterned Kami, a bit higher end but again widely available. The tessellations were also made form Kami, albeit in larger sheets. I'm probably the only person on Earth who does tessellations in this material, most use more expensive art papers. But I like Kami, and its actually quite a bit more difficult to fold than art paper. Again, widely available.
The two arthropods were made from specialized art papers. The centipede was made from Sekishu paper that I had treated with a solution of methyl cellulose, while the beetle was made from a sheet of Unryu similarly treated.