Questions about the Proof of Stake consensus

I'm trying to understand more about how Ethereum works after the PoS migration and ended up with a few questions I couldn't quite resolve.

Question 1:

With PoW there was a target block time of 13s which was adjusted by PoW difficulty. What the equivalent mechanism in PoS ie. how do validators know to wait until is a good time to propose a new block? I suspect leaders don't just look at their computer clock propose the block when it's time but I can't quite figure what they do.

Question 2:

Is it a desirable property to have blocks target a specific block time when they could optimistically propose the block when there are 50% or even 66% attestations from validators for the block. I understand that reducing the block time to only a few seconds could cause centralization with nodes that have access to better network conditions but if the requirement is to have attestations from 66% of the validators I don't see the issue besides not having a constant block time.

Question 3:

It seems that the Beacon chain holds information about the validators (stake queue, unstake queue etc) and it also part of the Ethereum node implementation. How does the Beacon chain differs from the main Ethereum chain? Is there a reason that is called Beacon chain ie. is there a different consensus? Does the Beacon chain also store the block attestations from the validators or that's only store in the blocks?