PPS is just a "payment structure" it doesn't have any unique aspect in regards to how blocks are constructed or handled
No, but it does matter for the DAO structure. Miners need to be paid regardless of whether they mine a block or not. That means their source of income is the coins at stake.
also, miners don't need to have to agree on a single block header, in fact, every miner hashes unique block header due to the fact that each nonce is different, the only thing that needs to match across all miners would be the coinbase transaction, it's how centralized pools know which share is "worth paying for" and which share isn't.
The pool must be giving a unique block header to each individual miner as well, otherwise there will be instances of miners hashing the same things (providing the same work multiple times). Nonce is a field they change later. Is the merkle root difference to each miner, or is there an extraNonce field which could be their pool ID e.g.?
That sounds like a good idea, the "representatives" would need to vote/decide which share is valid since any unfair player can submit shares to the pool which contain a coinbase transaction that pays to their own address and thus would receive rewards for the work which was never intended to benefit the pool.
That's correct. The only disadvantage of this whole business, is that there have to be colored coins issued; at least that's how voting process works in Bisq.