1) The bigger circumference of the tube/rail, the easier it will be to operate on skis. No need to build any kind of structure below it. If you want, you can screw on some kind of impregnated wood supports, but they're definitely not mandatory. Just tuck it in the snow. My backyard tube is 250mm / 9.8 inches in circumference.
2) 3m / 10 feet is the shortest I'd go. Mine is 8m / 26 feet. The longer the feature, the higher the need for speed of course.
3) It's round. It won't tip. It won't even spin. Just tuck it in snow the whole length and both ends.
4) Use the kind of tube meant for outdoor sewer / drainage pipes. Sturdy, heavy, and slick. My tube weighs like 50+kg / 110+lbs. You can find a few posts of it if you scroll back from this post showing the funeral of last season backyard setup on my Instagram;
https://www.instagram.com/p/CNCXqpXhw9f/