I've had that happen a few times. What I suspect is that another hen is on her nest laying an egg when she gets back from her daily constitutional so she gets confused and goes to the wrong nest. Then she doesn't move. When I see her on the wrong nest I move her back to her nest. Most of my broody hens will go back to their nest even if another hen is laying an egg in it but each chicken is different. You can never be sure what any living animal will do. I've had a hen off of her eggs so long they felt really cold yet that hen hatched 11 of 11 eggs.
I don't think so. Like others, I've had hens hatch in much warmer temperatures. I've seen hens stand in the nests when it is hot, like she was cooling her eggs. In warmer weather my broody hens often spend a long time off of the nest for their daily constitutional compared to how long a hen stays off in colder weather, but that hen is not going to a different nest because her eggs need to cool off.
I believe that you have two options. You can continue to move her back to her nest or you can isolate her in a pen and lock her in there where she can't leave until the eggs hatch. People do it successfully both ways. Of course, the risk of moving her is that you risk breaking her from being broody. Some hens move a lot easier than others. If you let her out a day or two after she hatches the chicks will still be raised with the flock.
I've had similar experiences and is why I don't believe in that first time broody or experienced broody stuff. I've had great success with first time broody hens and I've had failures from broody hens that were previously successful. Each time they go broody is a unique experience.
Who knows, it could be. I'd have issues if I were being bitten by ants. It may not have been another hen on her nest that originally moved her.
You can certainly try, but I'd want to be around where I could observe. They tend to imprint on the nest, not the eggs.