Good question. You have some solid thinking there about the trade-off between decreased surface area (collapsed gills) and higher oxygen in air. However, fish in air do seem to still be “gasping.” Lab tests show that fish released immediately or after 1 minute have about an 80% survival rate, but by 2 minutes, that’s down to 20%. Apparently, the extra oxygen in the air still can’t make up for the decreased surface area. The diffusion of oxygen into the blood is rather slow.

Being hooked and handled creates stress, causing fish to have a higher metabolic rate and need more oxygen and energy, just like how your heart beats faster when you’re scared. We don’t know if the fish are actually scared, but they produce the same stress hormones that we do, and these can be measured. Another issue is that the fish will probably be warmer in the air. Warmer temperatures speed up chemical reactions, like the metabolic reactions in bodies. This would create a higher demand for oxygen and energy. This is also the reason that it is better not to catch fish when water temperature is high.

Basically, the less the fish is tired out by being played, the less time it is handled, and the less time it is out of the water, the better. If you use a hook that you can remove quickly—like a hook without barbs, the fish will spend less time in the air. If you can remove the hook with the fish underwater, that’s even better. But one study showed that using a lip grabber on the fish when removing the hook can damage its mouth.

Holding the fish (gently) in the water until it has a chance to get oxygen into its blood can help it avoid being hurt while it’s recovering. When it has recovered enough, it will swim away.

So it looks like the best way to help fish to survive is to try not to wear them out before you land them, get the hook out quickly and underwater. If you have to take it out for hook removal, put it back in while you get your camera ready. Take the photo quickly, then let the fish breathe underwater before you let it go. The site I read also suggested using rubber nets without knots to avoid scraping off the protective mucus on the fish.

The best way to increase speed and efficiency at anything is to think everything through, have a plan, practice the moves you need, and make sure that you have everything ready to go. You can do a “dry run” before you are even fishing. What equipment should be ready before you land the fish? Which hand should you use for what? How can your fishing buddy help?

This depends a lot on the fish. Most fish can live out of water for minutes, but some can't live for more than a few minutes, while a few can live out of water for months.

The simple answer is that yes, a fish's gills can absorb oxygen as long as they remain both wet as well as not so collapsed that they are no longer exposed to the air . The high surface area also means that water evaporates quickly, so keeping those gills wet can be a problem.