Yes, an air conditioner can be repaired, but not all issues can be fixed with a repair. The problems you face with internal parts like a filter, evaporator coil, motor, fan, etc., can be repaired. The circuit breaker, insulator, or wiring issues can be fixed after a repair.
But if the Whole AC unit is damaged, replacement is a must. One important thing to keep in mind is that Freon refrigerant gas is banned in the US. If your AC unit is old and needs this gas, you have to look for a new AC system.