First, the horses have two different jumping styles..Levi is much flatter in the bascule which makes it easier to keep position. Tiny rounds more and gives a better bascule which, until you learn to ride it, is going to bounce you.
In the vid where you came off, you dropped the horse, put your hands on his neck, before he actually jumped..I am guessing this is a defensive position due to you getting bounced. You need to approach the jump in less of a modified two point; you are leaning TOO far forward in prep for the jump. When Tiny jumps, he is rounding more causing you to fall even further forward. You need to approach the jump with your shoulders a little more vertical.
In the second vid with Tiny, on the grid, you did fine over the smaller verticals..it wasn't until; you got to the larger oxer that you got bounced. Again, you were too far forward off the second small vertical and I think you got left behind a little..you also folded a lot more over that small oxer and it looks like you made a much bigger effort than was needed.
The last vid had an error of some sort and wouldn't run.
Correcting..harder to say as you have the basic jump position down. Heels, leg and head look good as does your level of release. Again, try approaching a jump sitting up more rather than getting into early two-point, or, if you need to get into early two-point, do not fold quite as much in the approach. You want to make a small move over the jump and not thrust yourself over it as though you are "helping" the horse to jump..let the horse come to you. An instructor of mine gave me a good visual..push yourself away from the horse with your hands. This gets your seat back in the proper position.