Those lifts from the hang are very good - you're right that you mainly need to pull down harder.
The last video of the snatches from the floor were definitely an improvement. You're a little behind the bar w the bar too far forward early in the lift and opening the hips too soon later. I would bring your hips up slightly and the bar back slightly in your start position. When yuo first break it off the floor, immediately get the bar back a bit and make sure your shoulders are not moving behind it. In other words, push with the legs without extending the hips.
Then wait longer/higher until you start the second pull. Way later than you think it should be. That's why you look better from the hang - you're in a good position to start the second pull. When you start on the floor, you blow right past that position bc the bar is forward and you're extending your hips too soon. Practice DLing to that hang position, then snatching, and eventually get rid of the pause.