So, for anyone familiar with the Final Fantasy games, you know how old gods and monsters are used as enemies/allies. Ifrit, Shiva, Odin, Bahamut, etc. Pretty much know what those things are. But, what the hell is Alexandr? I’m guessing that it comes from Russian folklore, but what is it supposed to be? Is it, as I think, a giant, steam-powered Cathedral used as God’s Mech?
The referenced Alexander is probably Alexander the Great, a Macedonian fellow of some importance. 
As for the source of the graphic…you got me; it looks like a massive edifice in the classic style rising from the sea and firing missiles (which do Holy-type damage). What exactly were the programmers smoking, and may I have some, please? All the other summons make some measure of sense (except maybe Eden), but they lost me with Alex.
Hijacking, I’ve always wondered – once in a while (in FF3) a tapir will appear at random to heal a party member. What’s up with that? Huh? I mean, a tapir?
Even more unusual, in Final Fantasy IX, Alexander makes an appearance and has wings that he uses to wrap around a city and protect it. He(it) looks nothing like it did in the previous games.
Final
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Spoilers
Yes he does. Aside from the wings, of course. And even then, he’s closer than Bahamut or Odin are to their earlier forms. The fact that Alexandria Castle is between his fore-legs/arms/whatever the heck they are might have thrown you, but that’s the same Alexander that’s been around for the last 4 games.
As to what Eden is (No idea what the deal with Alex is) - she’s a living Garden (She has basically the same structure as Balamb or Galbadia Gardens once they start moving, and, of course, we all know the Garden of Eden.).
There is a very good site with the origins of (most of) the summons, etc. in Final Fantasy. They haven’t updated with the latest games but check out http://userpages.umbc.edu/~kmallo1/origins.html
If you are interested in Final Fantasy, check out Final Fantasy Online at http://www.ffonline.com . They have a board like this one there as well.