For the first video, I think Hell Man had it. A small float plane has three rudders, one for the air and two for the water.
The two water rudders are at the end of each float, and they are supposed to be lowered only for Idle Taxi. A set of rudders that can steer you at a couple of knots are going to steer you really, really fast at 70 knots.
It looks like he just forgot to raise the water rudders.