For 1), I'd randomize with proportional unit (share) representation, and I'd certainly be open to rule-prioritized execution (e.g. most-favorable taker first) if it didn't lead to degenerate incetives. Smart market design can incentivize people to play at their best price. For example: locational marginal pricing in wholesale energy markets...
2) I agree that the real world is quantized, but I think that a settlement tock to the bidding tick could be used to reduce the value of proximity. IEX actually implemented general latency with long runs of fiber, which is a really elegant fix. They couldn't make the rest of the world latent, so it's something like 700 microseconds, enough to remove colocation advantages, but only enough to solve for New York.
3) As far as I know, HFT's like to play in limit order and derivative books. It's where practices like flashing and spoofing have come from. Market orders are fraught with peril, especially if you don't know the matching rules for the exchange. As far as tightening the spread and aiding price discovery, I don't think that those two things are the same. If a security has naturally low volume, responsive high frequency trading can effectively be predatory.
4) I agree that there is more to HFT than just speed, but I view high frequency temporal arbitrage as an unnecessary market feature that provides the illusion of liquidity right up until that liquidity would truly be useful (since robots get benched when things go strange).
Granted, the temporal steps that I'm advocating here are a little provocative. The US could be solved in something like 200ms, and larger global markets, like currency exchange, are already fairly decentralized (though not as much as they used to be, as far as I know).
Either way, I don't think that NASDAQ can assure global temporal coherence, especially without controlling the entire network. Given that, it makes sense to design robust systems that don't pivot into rare modalities in exceptional cases. Just pull clock slew off the board.