::'.done with the kitchen errands.' Otherwise it is likely that mother will never ever do kitchen errands again. As well, I would usually use 'chores' instead of 'errands.' : My mother is done with the kitchen chores.1. My mother is done with kitchen errands.
::for a more colloquial feel: "Mom's done in the kitchen."
::You don't want a comma in this sentence; it breaks the flow.2. How can you switch on the light, when there is a power failure?
::colloquial: "How do you turn on the lights when the power's down?"
::Grammatically this is okay. Any variations would depend heavily on the context in which it was said.3. I have learnt how to start a car.