Reward comes from penalties and fees, as I understand it. If you stake and then Lightning runs on top, you collect the fees there without the high costs if opening and closing channels on the main chain. It may be that your stake (bond) amount limit is tied to the liquidity you can hold in your Lightning channel. I may be wrong, but assume there must be a mechanism there, like a Watchtower that also contains one of the keys to the multisig for your peg-out. That seems feasible.

I'm also skeptical, but trying to be open to the possibility of a PoS which manages to avoid the issues you mention.

I'm not understanding the clock time point. An epoch can use the Bitcoin block height as a clock.