Sorry about the delayed response. I use an iPad all the time these days, and for some reason the post section doesn't trigger the keyboard to come up, so I have to write my post in 'notes' then copy and paste. PITA!
On the sheets question. Well, I'm a real comfort person. My husband once told me he's never met someone so devoted to their own personal comfort as me. I'm not sure whether that's good or bad! Sounds kind of indulgent. But anyway, I've done a lot of research on feathering the best nest, or in this case, finding the most divinely comforting sheets on the planet. Well, we have a big old bed frame from New Orleans that my husband bought when he lived there which has side panels around that don't allow a bedskirt, so that's not an issue for us. I've seen them on specialty sheet sites that come up from typing 'twin xl' into the search engine. For sheets, how long have you got? I could write a novel. Getting quality sheets to fit the twin xl mattresses is no problem. Just depends what you like.
If you're a fan of soft and silky, low maintenance sheets, I can suggest the lyocell ones from Sandra's site, which I think is called Snuggledown. She also sells those great Dormier wool mattress protectors that people here (including me) love. The twin xl lyocell sheets she sells are a very good price for Lyocell which tends to be expensive, are well made with elastic all around and stay on well. I believe their made by DeWoolfson. I have a lot of their bedding (down comforters/pillows etc) and can vouch for the quality. Just white, which I find great for sheets.
If you love to sleep cool and in a true luxury, I can't speak of my love for linen sheets enough. These days I've gotten quite a collection of antique French linen and to my utmost joy have found that even non-fitted sheets work perfectly well on the adjustable beds. The heavy weight of the latex keeps the sheets in place perfectly. So I've been sleeping in the bliss that antique linen provides. However I can tell you about a fantastic guy in NY who has a company called Linoto. He made us absolutely beautiful quality twin xl fitted sheets for a VERY reasonable price for linen. They will last a lifetime, and I can't describe just why linen is so great, but it just feels healthy, breathable, dry, silky. Keep in mind that new linen needs a bit of a break in period. It can be a bit exfoliating to begin with! After a few washes (with Linoto's it was just two washes and a bit of sleeping in them) they soften up and just get better from there.
I bought some of the most expensive sheets on the market. One of my favorite for cottons is Sferra. I bought their top quality Giza 45, and though I discovered linen soon after that outrageous outlay, I know the duvet cover will continue to get plenty of use in the winter time, as linen could never be so fine and light, which makes our duvet float on us like a cloud. Linen is heavier and I bet would weigh the duvet down a bit. But for summer, it's linen, linen, linen.
Hope I didn't respond too late, and that my suggestions as to where to find twin xl sheets helps. I never bought anything from those specialty sheet sites as they look cheesy. A far as bedskirts, if you're going to try the linen, you could ask Linoto to make them to your requirements as he custom makes all the bedding.