L1 Bitcoin will work just fine on interplanetary scales, you'd just need to wait for extra confirmations compared with Earth time. Mining would only ever happen on Earth, though (maybe on the moon as well). Planets could have their own lightning networks.
Sure thing! The problems I point out appear if mining decentralized among planets is attempted, which you would want if bitcoin is to remain decentralized. Otherwise, as space colonization advances, bitcoin will get increasingly centralized and likely dropped beyond earth, thus leading to a classic "international market exchange" scheme.
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