Proof of stake lacks the security properties of proof of work, e.g. via grinding attacks.

Grinding attacks aren't a problem if you include secure verifiable randomness in the protocol. E.g., Algorand's VRF-based sortition, or Ethereum 2.0's verifiable delay function.

Solves as in it does not use more energy than what the hardware needs to process the data + it doubles every time you double the number of nodes (obviously since they all have to do the same work too) Its not wasting energy for a PoW lottery it just uses energy like a comparable instant messenger with global server farm would. The more people who use it the more energy it will use there is no way around that.

FBA is completely different form PoS. It does not work on incentives and penalties it works with a global final state, global rules and (federated) byzantine agreement (FBA) for progress (adding the next "block"). No way to re-org, no block/staking reward, no censorship. If someone doesn't act in everyone's interest other nodes simply wont listen to them anymore. Not following the rules its publicly visible for anyone. And since there is no reward anyway there is no financial reason why anyone would participate who does not simply want to help the system.