We called that a front drop, and the one with the legs straight out in front, sitting down...a seat drop. Combined it was a seat drop to front drop. A seat drop, then bouncing up into a half twist, leading to a seat drop on the other side, was called swivel hips. I found those really fun, and I would do lots of them in a row.
I didn't like the backdrop, I was scared of it. Never attempted somersaults or backflips.