You still have all the basic kinds of units that normal Civ 2 has, but they are called by different names, and may not necessarily be humanoid. You also get nifty new units - like Dwarves, Dragons, and Trees in the fantasy world and the Bombus in the science fiction world (it's a giant bee that's great for exploring
and combat).
You can still improve your terrain to farmland, but again, it's called something different. A lot of the techs do the same function, but have different names, and some of them you won't be able to research, depending on which faction you play. You will need to steal them or trade for them - and in the science fiction scenario, you can't trade between humans and aliens until you have the technology to speak to them! So if you want their tech, you either need to be patient, or send in the diplomats/spies.
I'm not sure what you mean by having Civ 2 on your screen. Test of Time is a variation on Civ 2, and it includes the normal Civ 2 game, although the graphics look a bit different. As for odd combinations of units and transportation... well, I've teleported Dwarves to the Cloud world to speed up construction of roads, railroads, and mines, but they can't get there any other way. There's only one way to get a Buteo Settler to the Underground world - through the Gate of Hel, and have them build a city and hopefully not get killed off by a particularly nasty invisible worm monster that you can't see until it actually gets within your city boundary (but you can usually hear it moving for several turns beforehand - very creepy, wondering where the heck that thing is).
So yes, you can play the Bird people if you want, or an Elf, Goblin, undead Stygian, or one of the two human factions. Each comes with advantages/disadvantages as regards tech, movement, and combat abilities.
As for combining the worlds to have aliens trading with the Mayans, that is possible only in the Extended version, and it happens in the late stages.
Sending a camel caravan on a starship? Nope, unless you talk to the people who do modding. That's something beyond my capabilities.
If you have a choice, try to get a boxed edition that comes with a double-sided tech tree poster. It gives the tech trees for all the different worlds. I think somebody posted one here on the forum a few years ago, too, although I don't have the link anymore.