Ships docked in a hangar are in a sort of stasis: they use no maintenance supplies and their clocks never run. I use this in the form of "Stasis Box" PDCs on some of my worlds, storing particularly maintenance heavy ships for long periods of time with no mineral cost other then the PDC construction. I'm not sure what you mean by the second question, though I'm assuming you're asking if you can perform damage control using the mothership's maintenance supplies and refuel using the mothership's fuel storage. The answers to that are no, damage control can only be performed with onboard supplies, and yes, ships landing on motherships in my experience are automatically refueled.