No they are very painless solutions to make sure that no metal every passes past the reticulo-rumen.
Absolutely nothing.
Yes, magnets can hurt you if they are not handled properly. Strong magnets can pinch or crush skin, and if swallowed, they can cause serious internal injuries. It is important to handle magnets with care and keep them away from small children.
Your local feedstore or your local large animal veterinarian.
One is good enough.
Yes. Most cow magnets can weigh around a pound or two each, but often never exceed three.
Cows don't have "built in magnets." Magnets are inserted down the throat of a cow as a way to prevent her from getting hardware disease from eating too much scrap metal like nails and wire. The magnet in a cow works exactly the same as any "normal" magnet does.
Antibiotics can cause abortions if not administered correctly or given at a time when the cow doesn't need it. It won't hurt the cow, no, but it may hurt the unborn fetus inside her.
Some cows have magnets inside their stomachs! The magnets attract any metal that the cow might accidently eat, which would harm or kill the cow if it passed through the digestive system. A cow can keep a magnet inside the stomach for it's entire life without harm.
It depends on the cow. You can try to test it but it might hurt some of the cows.
Putting a magnet on a cow's face would not have any significant effect on the cow. Magnets are often used in some forms of livestock management to help prevent hardware disease by attracting and collecting any metal objects the cow may accidentally ingest. Cows have a tough hide, so a magnet placed on their face would not cause harm.
If it hurts a cow by drinking its blood, I bet it can hurt a human, but not life threatening.
Unless there's bits of plastic on the hat that may block the cow's digestive system on the way down and out, it shouldn't hurt the cow.