1) Eth2 has been "coming soon" for a long time, so it will never happen. (Yes progress has been slow, but it's happening, with phase 0 live now.)
2a) In PoS, the rich get richer. (Not true in a meaningful sense. Staking rewards are neutral with respect to economic inequality, since everyone has access to the same rate of return.)
2b) PoS is a social issue. Climate change is also a social issue. Therefore, a PoS is a climate issue. (This is a converse error.)