Getting to understand it .. a few questions.

To make foot not move, you can use a pin (looks like a push pin icon at bottom of rigging panel) - yes, using the one you show in video. A stick stops warping, not movement. But if you pin it, the foot wont move. Another trick if you cannot pin it is put out a dragger on it and record a drag movement of the feet. That will hold it in place because of the drag recording, but remove the drag recording (e.g. trim it in timeline panel) and it will move again.

The two feet move together because you put a stick across them both. That says to keep them unmoving relative to each other. Remove the stick and the feet will move separately. Pin one foot and you can move the other foot still.

The foot before probably did not move because it had a fixed pin. So dragging the toe will not move the fixed pin (so foot stretches)

To make the tail move better, when you click on the tail layer there should be a property "Attach type" which i think is set to weld. Try changing this to hinge so it rotates where the tail connects to body.