I already have answers for 6 and 7, but would like to know about the others (including the spin-offs)

1. Does any of the Civilization games have any limited time, exclusive, or promotional content, even for owning a different game? (I think 6 and 7 have rewards I can't get anymore)

2. Is there anything permanently missable in any of the Civilization games? I know they require multiple runs, but I still want to ensure there's nothing that would require completely starting over my save.

3. Is each game identical across all releases, and for entries with achievements do platforms that lack them have an in-game equivalent? (Revolution has different achievements between the 360 and Apple versions, and I don't know if one version still rewards you for the other list.)

No, the earlier Civ games come from a time before that kind of thing was commonplace. Before digital distribution there was no practical way of having this kind of promotional or time-limited content for PC games. The only thing I can think of are wonders. Only one civilization can build a wonder, and if someone else beats you to it you can't build it yourself. Civilization 2 has the original and Test of Time releases. They have very different art styles. Test of Time adds a lot of new content, but it also introduces a lot of bugs so many people consider the original release to be the superior version.