What is called the exercise in which you fix your feet to, say, a wall and then change your position repetitively from seated to lying?
Please tell me of other exercises like this. (Those that doesn't need special instruments, like jumping jacks, and push-ups)
After that, if you wanted to name some with instruments, no prob! :)
That is most commonly called a sit-up. You will also find it as one word (situp) or without the hyphen. However, that exercise has fallen from favor. Instead, experts prefer the "crunch" (abdominal crunch) which is a modified sit-up with less risk of injury. Some now call the new version a sit-up.
When I was a child, we had one that has also fallen out of favor. It is call the squat thrust. It can also be combined with a push-up in the middle.
The squat thrust starts from a standing position. Then you squat straight down and plant your hands on the floor to your sides. With your weight on your hands, you kick your legs back to assume the starting position of a push-up. (At this point some add an actual push-up, but that is not strictly part of the squat thrust.) Then you kick your legs back to the squat position. Finally you stand up.