Shuts off while driving

Hey! I am having trouble with my car. What happens is that I start the car (with a little fight, need to twist the key for a second) and drive away. After a few hundred meters the car shuts off, when I push down the accelerator pedal nothing happens and the speedometer is lowered to 0. The instrument panel lights start to shine with a solid shine. Oil lamp, battery light and engine light. I first suspected the generator, when I have a mobile charger and charged the battery, it worked to drive the car again in a few hundred meters. The longer the charging time, the longer the driving time. Took the car to a mechanic who, however, read the error codes:

P0700 - Transmission control.
P0741 - Torque converter could.

Could it be above error codes shutting down the engine or could it be something else? These error codes come and go.