I've read studies published on the Internet by fishery biologists that show that gill-hooking has a very high mortality rate- like 90%.
Most of the important stuff about releasing fish in good condition has already been covered: use barbless or debarbed hooks, wet your hands, don't squeeze, keep the fish out of the water for only a few seconds, put the fish carefully back into the water instead of just tossing it in the air.
Turning fish upside down does help to calm them down.
I've never been able to get the hang of using forceps for hook removal. But some sort of tool is a good idea for deep-hooked fish. This year, I'm going to try a lobster fork- those little forks with two short tines.
If you can't unhook a fish after a few seconds, put it back in the water to swim a little bit and try again. If it's too hard to get the hook out, cut the leader off.
One point that osprey brought up: in the winter, be very careful with handling. In subzero temps, their gills can get frostbite quickly, which is a death sentence. Laying them on the snow is a bad idea, for the same reason. It's always best to keep fish in the water to unhook them, but it's an especially good practice when the temperature is below freezing. If you have to take a fish out of the water to unhook it, be quick about it.
As far as photographs: I sort of leave it up to the fish. Some fish are okay with posing for a second or two, some don't like it. The camera-shy ones struggle, and I put them back without delay. I prefer to get pictures of fish in the water anyway, but they often scoot. Oh well. I take fewer fish pictures than I used to. If it's too much like work, I don't bother.