You would adjust the speed with the slider, yes. They will be powered by that molex when it's connected to the power supply. The loose ends are where the fan cables plug in. (The ones you're holding at 25 seconds in on your second vid are what I refer to here.)
The case fans will have their own wires that end in connectors that should fit the ones you have. Look at any of the fans and follow the wire from it to the end.