Silicone craft mats are made from silicone — product descriptions commonly list the material as silicone and note that the mats are waterproof and lightweight.
Yes. Many silicone craft mats are lightweight and designed to be foldable or rollable for compact storage and easy transport; some descriptions explicitly note they roll up for storage.
Smaller options shown include an 8.5"×11" clear tracing mat and palette/mixing mats such as 7.5"×11" and 10.5"×12".