Would you need a power source? If you aim your ship correctly, then put everything alive into cryo, the ship could go completely dark, vent all heat and become a frozen rock. Then after [very long time] the ship enters the vicinity of a different star and can be reactivated and unfrozen using solar energy. You dont need energy to maintain cryo if the whole ship is at 1° kelvin.
(Of course that relies on cryo sleep being possible)
Only if they can be turned off (same as the cryo sleep). The whole ship either has to have enough energy to last potentially 100000 years (no theoretical power source exists like that) or enter a state of 0 energy consumption. Solar/radiation collectors dont work if you are to far from a star. Synthetic life still needs energy