Electrics/battery/wires and no start issues

Last week my battery light came on and then went out, a few days later after giving the car a thirty minute run twice it would not start. Started fine the next day so I drove it to work, when I got home from work (only a fifteen minute drive) I stopped the engine and wanted to double check it would start again and it would not start. Called the AA and the guy said there was a loose wire so he soldered it back together and fixed it, said I may need a replacement battery but to give it a good run and it should charge it up. The next day it had its MOT and nothing showed except welding - which cost me £354 altogether, then a few days later it would not start again, went and got a brand new battery fitted, a few days later the battery died again so I called the AA out again and the guy said the wire which had come loose before (connect to alternator I think) was causing the battery to drain while it was plugged in and then while it was unplugged the battery was charging, he told me I could drive with the wire unplugged for a few days until I got it fixed and to leave the car running on the drive for thirty minutes, when I went to turn the car off it had overheated. I drove it to work the next day, my radio was not working, my heated rear window wasn't working, it was not telling me how fast I was going, every time I changed gear it would make a ticking noise, my battery light, ABS light and engine management fault light were all on and after ten minutes a temperature light came on and the car started to get really hot (would not blow cold air out) and it smelt really bad, luckily this was just before I got to work. I plugged the wire back in and now it will drive but my battery is being drained and my main lights are not working. I know nothing about cars and do not want to be ripped off and do not see the point in paying loads more money on this car when it is causing me nothing but problems!