Big red ants are not usually harmful to pets or people depending if you or your pet has an allergic reaction to the formic acid that it secretes when you are bitten. You should be more concerned about the smaller ants since they secrete more formic acid.
Yes, big red ants are fire ants and they are somewhat harmful to people or pets. They will bite you and where they bit you will be swollen and poofy for a few days. And it will hurt. But it will go away in about a week.
Yes, the ants you speak of are also called fire ants. They sting you. One sting is nothing much but when stung as a colony, which is how they attack, it can be very painful, if ingested they will sting your air way which will cause it to swell and put you in the hospital or worse.
yes they can be harmful, if provoked they will bite and it will sting you badly, this can cause alot of pain in the person or animal, but do not worry, this pain and swelling will go away in a few days