AWG 2/0 copper wire.
200. Although you cannot exceed current ratings on any branch circuit without tripping that circuit. You need to make sure that you do not exceed 160 continuous load amps to meet NEC requirements of not overloading a breaker to more than 80% under continuous load.
You need to be more specific. Do you want a contact telling you if a circuit breaker is on? If that is your question, the answer depends on the model of the breaker.
A circuit breaker must be reset to ON after a short circuit but does not need to be replaced. It depends on the type of CB. A fuse is also a circuit breaker and it needs to be replaced after a short circuit. Relayed circuit breakers have to be "picked up" after a dropout and need not be replaced as such.
For your electrical system, you will need a circuit breaker that matches the voltage and amperage requirements of your appliances and wiring. It is recommended to consult with a qualified electrician to determine the specific type of circuit breaker needed for your system.
Usually a 15 or 20 amp breaker is sufficient
A circuit breaker is designed to 'break' in a circuit if a short circuit (or other malfunction) occurs. This prevents overheating (or burn-out) of the circuit wires. In older systems, you would need to find which fuse wire has fused and replace it. In a circuit breaker, once the fault has been found and corrected, the breaker is simply switched back on.
The circuit breaker is sized to the full load amps of the motor times 250%.
If the circuit breaker is in the off position there is no need of overload protection. Overload protection monitors the load amperage, If there is no amperage through the circuit there is nothing to monitor.
Not if the GFCI breaker is supplying the circuit you are wanting to put the GFCI receptacle into.
I need short circuit calculaion
A dryer does not require a quick disconnect breaker. However, it is recommended to have a dedicated circuit with a proper circuit breaker for the dryer to ensure safe operation and to meet building code requirements.
No. The breaker must protect the circuit components such as wiring, outlets and switches that are connected to the breaker. Therefore if you have a 30 amp circuit as dictated by its components you need to protect it with a 30 amp or less breaker.