Car braking itself while downshifting

That is completely normal. When you take your foot off the gas the car will start slowing and it uses the engine to assist with a process called compression braking as it shifts to lower gears. In neutral the engine is no longer connected through the transmission so you get no braking and need to rely only on the foot brakes. No a real safe thing and illegal in many places as they consider it coasting without control. That is because you can only apply the brakes, but if you needed to accelerate you have to shift back into gear first. I would however caution about doing a lot of hard acceleration, the transmission in them isn't the most reliable item in that usage, of course neither is the engines valve-train as there are many that have failed parts in the upper engine as well.