The shiny part goes on the inside, toward the baby. No matter if it's sandwiched between fabrics or if it's the outside layer of the diaper/cover/etc.
The best way to care for it is to wash on hot (unless your hot water tank is HIGH, then I'd wash on warm. You don't want it to be TOO hot..).
For a new diaper, you want to dry on hot just to seal the PUL from sewing so you don't get leaks. After that, you'll want to lie flat to dry if you can. Hanging can pull at the elastic and ruin that quicker, drying on hot can melt the pul. I do not lay mine flat to dry often--I just don't have room. I put them in the dryer with my dipes on a 2nd run through. I put my cotton/bamboo/etc. in the dryer on hot for a full cycle then for about 1/4 to 1/2 cycle I put my covers in with the other dipes to dry the covers/pockets and finish drying the cotton/bamboo/etc.... My washer is usually between 1/2 to 1/3 full when I wash diapers. I have been CDing for 3 years and the only covers that have had problems with my wash/dry routine is the Bummis Super Whisper Wraps.. They're still waterproof but they're kindof shriveled. I have covers I just bought from Fancy Pants on Hyenacart and they're my alltime favorite (the BEST covers!) and I plan to lay these to dry as much as possible because they're one-size, my kids are so close together, and I want to get as much use as possible out of them with them still being functional when I'm finished.