Your city should be able to get to size 12 without a hospital. If you're short of food there, irrigate some grassland or plains tiles until you have enough.
Besides espionage, what techs have you researched so far? When you're trying to get ToE, I generally just research steam power->electricity->RP->medicine->scientific method. If I want to use US as a prebuild for ToE or Hoover, I'll snag industrialization, too.
What government are they in now? If it's fascism (which is likely if they've been as aggressive as you say), they don't get war weariness.
As vmxa said, chopping doesn't speed up wonders, and neither does disbanding. Unless you've got a prebuild for ToE or can build it faster elsewhere, switch US to ToE when scientific method comes in as Aabraxan suggested.
Hard to say. How much more advanced? Do they have infantry and artillery? What about tanks? What do you have? It might be good to start a thread on this game and post a save--there's no "quick answer" for this one.
Thanks for the answers everyone. I'll try to fill in the details...
-The problem is I only get one sheild (if even that) on some of those tiles so it slows down my build in what is a drag race. (The Mayans are also building it).
-I am up to Industrialization, Electricity, and Scientific Method. I made a mistake and called the wonder Theory of Evolution scientific method in my earlier post. I actually meant that the Hittites are 3 turns away from that wonder as well. I really wanted the free techs that comes with it, as I am 2-3 techs behind the Hittites.
-They are in communism. So you are right, they do not get war weariness. I get an abundance of it however if I do not funnell all my funds into luxories. This is why the Universal Suffrage is so valuable to me, and why waging war to get it would actually hold me back a bit. If there is another way, I need to take that other way.
-The problem is (As just mentioned) they are 3 turns away from ToE. I am behind on both wonders, as they got the techs just before me.
They have replacement parts and have Infantry. They also have Coorperation and I think they are about to get another key tech. I have tried to trade with them and other civs for replacement parts but no one seems to want to give it up. So if I research it at 70% I can have it in 7 turns.
Thanks for your help guys! I'll take the advice you give me and let you know how it goes.
Oh, one more thing. The are across the ocean and with only 4 ships in my arsenal, you can't even say that I have a navy. I've been too busy smiting my enemies Egypt and Persia.

(This game is kind of like real life hystory. Crush Egypt to the left, then Persia to the Right.

)