pick it up
Some roosters will try for a few days or weeks after she stops laying but will find it is not worth the effort, pain and suffering he will endure. The non laying hen will not cooperate and will fight.
Yes, it's normal. Your Rooster is just protecting your hen while she's laying.
There really is no need. The hen will turn them herself when she's laying on them. She won't let you touch them anyway when she's sitting on them.
Remove the eggs. You can replace them with eggs you know are from another bird who was active with a rooster. Your broody hen won't care.
sitting
The hen lays the egg. The term "hen" refers to a female chicken, and it is the female that is responsible for laying eggs.
Chasseur
When the hen is laying to fill up her nest, 1 per day. When she's actually sitting and taking care of chicks, she doesn't lay ANY. That's why many breeds are bred to be 'non-broody'.
Resting a hen for a second laying production is called a molt. Chickens do not produce eggs when they are growing their new feathers.
The hen who is laying will have an inflamed comb. When they stop laying or aren't laying yet, their combs become a pinkish-pale color.
That would be a hen that lays eggs, or one that is used for laying eggs as opposed to one raised to be fattened and eaten.
A hen past her prime laying years can and will still brood. Even if she lays no eggs herself she will sit there and collect eggs laid nearby.