What neither of us knows is whether your mom is just playing with these fantasies or if she intends to act on them. The best case scenario is that she is bored, has no intention of following through and is just playing games. The worst case scenario is that she is intending to meet up with people who will initially be charmed by her stories and then angered by being played.
I think you do need to have a straight talk with her about what you discovered and your concerns. Do not approach her with anger or judgment — just concern. Do not get drawn into a battle. She’s an adult. She has a right to live life as she sees fit as long as it doesn’t endanger her life or others. Ask for reassurance that she is going to keep herself and the family safe.
Meanwhile: Just because your mom invites you to a fight, doesn’t mean you have to go along. The fights only escalate because you decide to participate in them. You really don’t need to fight. Your brother doesn’t need to fight. Your grandmother should not have to step in to settle family arguments.
If your mother provokes, just calmly state that you aren’t going to fight and leave. Leave the room. Leave the house if you have to. But don’t fight back. You already know it doesn’t get you anywhere. It just stresses you out.
I hope you are looking into a way to finance your education that will let you leave home. Work. Apply for grants. Talk to the financial aid office at your school. If you really do need to live there, arrange your life to minimize contact with your mom. Study at school. Work out at the school gym. You and your mother have a better chance to be friendly if you aren’t in each other’s space. You can live more peacefully and you can give your brother an important lesson in how to manage the situation.
I wish you well.