Mini - Cooper :: Overheating / Temp Gauge Rising / Battery Light Came On

I got my 2003 Mini Cooper out of the shop about 3 weeks ago.. They replaced the damper, the serpentine belt, thermostat, coolant gasket seal, rear rotors/breaks, bleeding of the breaks, and inner cv boot. Noted to get the oil pan gasket replace which i planned on doing in the upcoming week when i got an oil change but they put beside it was light leakage. All Power Steering was redone under a recall warranty mid July.

Yesterday earlier that morning my battery light came on but than proceeded to try off by the time i was back home. I drive my car in the afternoon, i notice that my battery light is on and continued to stay on. Then my temperature gauge goes all the way up. i open the hood, its nothing noticeably different. I sit there for quite some time and i drive it again to see if it would overheat. I drove about 3 miles to my in-laws and the car no longer overheated. I decide to drive it down to the AutoZone to check my battery and she tells me it weak to leave the car running to see if it recharges but thinks something pulling on the battery. (the battery is new barely over a year old) During the drive to the autozone and back to my mother in laws the car doesn't overheat but the battery light remains on. I leave the car running in the driveway a bit later i notice the car is smoking, literally hear the antifreeze boil in the car,antifreeze is all over the ground, and the temperature gauge is running hot but the cars fan was not running.

i'm not sure if these problems are connected but i never had either of these problems prior to get it worked on. My car has always started strong. The alternator could be going but all lights, electronics,door-locks, windows, heated seat are working. Furthermore, the car starts so strong every time, haven't had any symptoms of a bad alternator.I read it could be a belt issue but the belt and damper are newly replaced.