Can you recover Pokeballs that miss when trying to catch Pokemon?
No, every throw regardless of if it misses, hits and breaks out, or hits and captures will use 1 of which ever Pokeball you're using.
Every time you throw a Pokeball, it is subtracted from your inventory and you will not get it back, no matter what.
Tapping a Pokeball does not recover it. Instead, it just despawns it and allows the next throw to happen quicker.
Pokeballs are common enough that losing a few won't harm you at all, fortunately.
I have not seen any mention of any way to do so. I presume they expect you to continually restock PokéBalls by visiting PokéStops and spinning the picture - I've collected a lot of Pokémon (thus have thrown a lot of PokéBalls) and have never gone below 100 PokéBalls available (you often get 3 when interacting with a PokéStop).
It works for me on great balls but I haven't tried it on anything else. I also had the ar off. If you recover it, the ball glows and disappears from the battle field. I believe there was also an animation at the bottom of the screen but I only caught it out of the corner of my eye so I didn't see what it was. I know it worked because I encountered a Pokemon having only 2 great ball left. My first throw missed; I taped it as it was rolling and it glowed and vanished. I caught the Pokemon with the second great ball. When I finished I checked my bag again and low and behold I still had 1 great ball. So I know for sure that it works with great balls.