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How is that physically possible? How can an exchange make sure that I, living in Europe, get to see Bob's order at the same time as an HFT set up in a building adjacent to the exchange?

Easy, trading cycles occur in (e.g.) ten second intervals synced to UTC atomic time. For instance results of trades propagated for five seconds, orders are accepted for five seconds and then are executed. This should allow enough time for reasonable latency and ensure that everyone has the most recent price on the exchange.

At the same time I'm arguing that HFTs actually improve this situation (of market participants sharing the same information), instead of hinder it.

I decline to respond as I'm still undecided as to whether this is a good thing or not.

It depends on what the prior probability of them waking up without intervention was as to its significance. Statistical significance is a function of both frequency of effect and magnitude of effect.

What if instead of building warehouses, you offer to outfit most local stores with helipads / charging stations and POS data interchange so that orders from amazon can be fulfilled via local stores that then load and launch drones?

This sounds like a good idea but it isn't (for now). Look up "Currency Areas". There are several economic factors that are essential to make a single currency successful. One of the downsides of a global currency is that if someone is indebted to someone else, they can't print money until the debt is paid. Not only that, but it creates issues when labor forces aren't liquid geographically and trade isn't free between places. The value of the currency will start to benefit some economies at the expense of others, leading to inescapable stagnation (this is one of Greece's problems).

FWIW many economists were skeptical of the Euro zone because it failed to satisfy some of the criteria of a currency area. This resulted in problems for some of its members following the 2008 crisis.