Finding multiple End cities

Yes, more end cities are spawned.

On a server I play on with a couple other people (vanilla with spigot), we have found approximately 8 end cities so far.

It did take a while to find them all, but so far about 7 people have elytra. (a couple fell in the void)

I can confirm that multiple end cities spawn, and have in fact found three within renderable distance of each other. However, not all end cities contain end ships; I've found about a dozen cities so far, but only 6 of them had ships.

Yes. When you kill the Ender Dragon, 1 portal is spawned up in the air to get to an end city. To spawn the dragon again, place a few end crystals (crafting recipe here) on the portal to spawn another dragon. When you kill that dragon, another portal is spawned, and on and on.