My battery died 5 days ago, at which time I purchased a new battery. Today, battery was dead again. Got another jump, and had to go to a meeting. When I left meeting, battery was dead again. Another friend tried to jump start my battery. He did not know what he was doing, and he did not connect cables correctly. First time it heated up cables, melted part of the cables & smoke came from his battery. He thought it was bad cables. We had another pair of cables & he connected them wrong again with three of us women telling him he was doing them wrong. This time there was smoke, and a little flame. My question to you, is this going to damage my car and his. My car is sitting where I left it, and I will get it towed to my mechanic. I'm very worried, because I love my little car. It only has 42,000 miles on it.
Connecting the cables incorrectly could have damaged the car, see what the mechanic tells you. As for the dead battery issue it sounds like you have a charging system not working (alternator) or something (lights etc) are staying on all the time to drain the battery.
If you have a bad alternator or problem with the charging system on your car there should be a warning light on your dash. If there was no light then it's more likely you have a battery drain from a light left on or a broken component which is sucking power even with the key off. Map lights being left on are a typical case, there could also be a broken switch not turning a light off when a door is closed. There's other possibilities, if you are handy with a multimeter you could track this down yourself, otherwise let your mechanic do it.
Regarding the crossed jump leads, this is easy to do once but hard to do twice, I wouldn't let your friend near your car again. It's possible your car was damaged, if so there would likely be visible melting of the insulation on the wires going to your battery, which would indicate they heated up. If this is the case you need to get it fixed as it's a fire risk. It's possible the battery was damaged, a battery test would definitely be in order, if there's any sign of damage then replace it.