Hello, my name is XXXXX XXXXX I will try help you with this.
I would suggest you have the idle speed checked for the cutting out problem. Also check the throttle body is clean and doesn't stick slightly.
For your other problem I would suggest having the battery and charging system fully tested.
This includes checking cable connections and the engine earth lead.
Do you think it could be an alternator problem as well?
I am not sure you can know if is the alternator?
The alternator is part of the charging system.