Nets are for Googans. If you get on the river regular you can't be bothered with a net.
And to that, I say you're a idiot.
I carry a net all the time with me now, after many years of not carrying one. I bush crash and hike 20+ km/day with it in canyonous river on the island, through the thickest, most brutal bush you can imagine. Never has it bothered me in the last 2 years tucked away in my wading belt - not once. I have fished 50 days since Jan 1 - would you consider that "getting out regularly on the river?"
It makes landing fish easier for us and the fish. They don't go on that one last run that tires them out considerably. That's why you'll never see me being able to post a photo of a fish laying beside my rod without a hand on it - they aren't EXHAUSTED. Every fish I land, as soon as I loosen my grip (and I need to keep a tight grip), it gives me a shower. That's the way it should be. If you can make a fish sit still, and need to revive it, you're doing something terribly wrong imo. Plus, a net allows you to keep a fish in adequate water while getting a camera ready, rather than on its side in shallow water smashing itself while you fumble around.
To each their own I guess. I have a lot of guys scowl and leave when I walk in he head of a run with a spinning rod too cause "it's for googans/beaks." You'll never guess how many fish I quickly pick up behind them. I guess a spinning rod and a net makes me a double googan
Anyway...
1) Yes you can take a fish out of the water. My rule is 10 seconds max (when I've timed my lifts on the go pro, they are often in the range of 2-5 seconds). If there is no water pouring off the fish/your hands, it's been out too long. If you want to take more than 1 picture, make sure you let them take a decent breather before your next quick lift.
2) Wet bare hands are fine on fish. Glove are not. Knotless nets or rubber nets are best if you want to use one.
3) I try to never land fish in less than knee deep water. Obviously you can't ALWAYS do this, but it's a good practice. I would say you should never bring a fish onto shore or over shore unless you are killing it.
4) If you're talking about 3 seconds for having fish out of the water, then I would say both yes and no. As I said, I do it as quickly as possible. Typically this is 2-5 seconds. Anything over 10 is too long. Most studies focus on 30 second or more time intervals when looking at mortality, and even 30 seconds causes significant damage. Any air exposure is bad - limit it.