For hammock making, almost any fabric will do as long as it doesn't stretch. You're in luck where you are, actually, because silk would make excellent outdoor gear. It is not often used for outdoor gear only because it it cost prohibitive. Taffeta can be made of many fibers, including silk, but, here, it is often a polyester silk look-alike.
But silk is an ideal outdoor fabric, being extremely strong for its weight (parachutes were once made exclusively of silk), small to pack down and comfortable against the skin. For this reason, it would make excellent quilts as well.
Don't get too hung up on fabric content. Just shop for fabric by feeling how heavy it is, making sure it doesn't stretch, scrunching it up to see how it packs down and yanking it between your hands to see how strong it is. If you can find refined (not raw) silk--that is, the thin, shiny stuff, not the nubby stuff, you'll do fine for a hammock and quilts. If you find nylon, it doesn't have to be ripstop.
As for tarps, well, that's another issue. Unless you're going to waterproof your own, you're going to have to find something waterproof.
I'm no expert, but that's my understanding. I'm sure others more knowledgeable than I will chime in. Best of luck to you!