That's a great question. I often find myself skeptical about the order when it just lines up word-for-word. Like, "that can't possibly be right". But I agree, I think this is correct.

It is the most correct way to say it in German, and honestly, no obvious alternative springs to mind (and anyway, any alternative would be less common that the above phrasing)

No - nicht goes before a predicative adjective (one after "to be"), so it has to be nicht groß genug.

only in extreme cases.

That’s just not how we say it — we put genug after the adjective.

As in English: we say “big enough”, not “enough big”.

I'd love to know if/when "Die Großstadt" would be used...

Certainly much less than "city" in English.

Usually, both "town" and "city" will be Stadt. (There's no hard-and-fast, uniform distinction between the two in English, anyway.)

Großstadt is probably only used when you specifically want to emphasise that some place is a major city. For example, "There's no hospital in my city; we have to go to the nearest major city to get treated" In unserer Stadt gibt es kein Krankenhaus; wir müssen zur Behandlung in die nächste Großstadt fahren.

Reicht is a form of the verb reichen (be enough, suffice).

For example, Das Geld reicht nicht (The money is not enough; the money does not suffice).

Here, there is no “is enough” and so reichen cannot be used.