Order is simply a consensus. It has not much to do with time. In fact, transactions don't even need to be time-ordered. If there are no double-spends, their order is automatic.
If there were no double spends, we don't need a blockchain, or bitcoin or anything fancy. But guess what?
But that's all that is needed; order. Not "real world time". Of course, IF you tag real world time to transactions, you automatically get an ordering. And IF you tag real world time to consensus pictures, they are of course also automatically ordered. But it is not a necessary condition.
Trustless ordering cannot occur without a unforgeable proxy for elapsed time.
In order to avoid this, one needs to make sure that nobody is accumulating hardware capacity without using it. Bitcoin is only protected if one can make sure nobody has a significant amount of unused hardware. If one has a huge pile of unused hardware, one can switch it on and outperform the existing system with not much more proof of work than was put into it.
So bitcoin's ultimate protection is not by proof of work, but by proof-of-non-existence-of-unused-hardware. See, the attack of piling up unused hardware is obvious in PoW.
No one piles up unused hardware because there exists a competition to mine; mining is, on average, more profitable than attacking the network, that is the key of why PoW is superior to PoS.
That really depends on the PoS algorithm. It would be a stupid algorithm that doesn't allow staking.
No it doesn't depend on the PoS algorithm; block producers are elected by stake, and to prevent that election happening repeatedly as stake moves around (creating attack vectors), stake must be bonded in some way by preventing new blocks from being produced right away. So if you send your stake to yourself, you're subject to that bonding period. If everyone does that, no one can produce a block and the network stalls, forever.