Do you have any longer videos that show more of your paddle and pop-up?
Your feet! You are not moving them! You have to move your feet! Make sure you are in a stance that allows you to move your feet (video 3 - poo stance). Like dtc said, it looks like you are positioned too far back on your board, in all three videos the nose of your board is out of the water causing you to stall the board, wobble, then white water or wave reforming catches up to you and knocks you off the board. You could try this:
1. Lay further up the board while paddling so you pop-up closer to the front of the board
2. When you pop-up throw your legs forward and under you so your feet land closer to the front of the board
3. Once you pop-up shuffle your feet towards the nose to pick up some speed to get away from the breaking part of the wave.
4. If the wave gets steep (video 3) then you can shuffle backwards to lift your nose away from the water and avoid pearling.
Shuffling forwards and backwards on your board to speed up or slow down, or pull your nose out of the water if it gets steep. Once you feel comfortable moving up and down the board, you can learn to position your body weight on the board for a small trim turn, or setup a large carving turn. You need speed before you can do a carving turn.
Pmcaero mentioned an angled take-off, if your board is already turned slightly when you catch the wave, 1-o'clock or 11-o'clock, in the direction you want to go, you only need to turn a bit more to trim down the wave.
Practice catching waves and turning while laying down on your board, using your hands to put pressure on the inside or outside rail to adjust trim while on the wave.
Surfsimply has some great videos that you can study to work on your technique and practice new skills.
http://surfsimply.com/surf-simply-tutorials/Watch the first three videos before you watch the video on trimming and carving turns.
You are improving, way better than that video you posted in July!
A good way to practice your footwork is to catch an unbroken wave and ride it in all the way to the beach, even after the wave breaks it will force you to move your feet to keep the board gliding as the wave flattens out, if the wave reforms, it will force you to adjust again as it gets steeper. Once you understand the sensation of the board gliding and how to keep it gliding, you can work on a gentle lean turn to trim left or right in the whitewater. Once you learn how to gain or maintain speed on an unbroken wave you can shuffle to the rear of the board for a carving turn.
Learn to glide first, then turn.