For number 2, first, check both of the battery terminal connections are clean and not corroded. Next is to have the battery load tested and the charging system tested.
The left turn signal is likely a different problem. You may have a loose power or ground wire. It could be a fuse problem too. Have you checked to make sure all the other lights on the car are working? A mechanic would use a test light or DVM to check for voltage at the bulb terminal.
Cooling fan problems are often in cars of this era are often caused by a failed coolant temperature sensor fan switch.