No. Fertility occurs in the middle of a dog being in season (about the second week of the three weeks she'll be in season).
Thinking is that, if possible, you should not let a dog (bitch) get pregnant in her first season.
No a dog will not "nest" if it is not pregnant unless something else may be wrong with it so if your dog is nesting i would consult a specialist
It is not possible to spay a pregnant dog without killing the unborn puppies.
A dog must be in heat to get pregnant. Heat is basically her ovulation cycle.
NO
It is called being in heat or in season, is when the dog can become pregnant. No there should not be any signs of a fever. The normal temperature in a dog is 101 to 102 degrees. If your dog is running a fever while in heat, I would take her in to be checked out by a Veterinarian.
YES!
Get it spayed. Spaying a dog means removing its eggs.
Yes. Your Vet easily can. If you know there is a chance the dog is pregnant, immediately take her in and get her the (usually) one injection as soon as possible. The earlier the better. Dogs are like people in this respect -- you can abort an unwanted pregnancy without being "fixed".
Yes.
Yes, check with your vet. Only if the pregnancy is too far advanced it may be risky for the mother. But it is so important as a means to stop more unwanted puppies being born (and their puppies and their puppies...). When a dog is in season she cannot be spayed (too risky), but when she is pregnant yes.
Yes, a vet can 'Fix' a dog at anytime. I had my dog fixed when she went into heat. If she got pregnant, they can even take out the babies. It's pretty simple to do. Being in heat doesn't interfere with the procedure.