I've taught swimming and treading water for a long time and I also use your "do nothing drill". It really teaches students that for most people if you do nothing (i.e. - simply hang in the water with a little air in your lungs) you will not sink to the bottom. Instead you will simply float usually with your mouth and nose just slightly below the surface. Hence to tread water you only need to kick with legs or push down on the water to lift your body about 2 inches up until the mount and nose are above the surface. And for most tipping the head back will also accomplish getting the mouth and nose above water enough to get a breath. The "do nothing drill" is a great method that gives the student huge confidence. And permission to stop and do nothing for a bit if they get tired.
Irena, we all float differently, in the video you show yourself floating on your back horizontally aligned with the water surface - you have amazing buoyancy! When I float on my back my body hangs straight down vertically, only my eyes, nose and mouth are out of the water, just barely- I have almost no buoyancy. When you teach others how to swim or tread water you have to realize that learning these skills is SO MUCH EASIER if you float! I don't think many talented swimmers understand this since swimming has always been easy for them due to their high natural buoyancy. Thank you for your videos.
Ideally, you should be breathing normally, relaxed like when you're walking, that comes with practice. Having that air in your lungs helps you float, so breathe out and back in quickly, that's a good starting point. When you breathe out your body will go down a bit, unless you offset that with a harder kick or arm movement.