I was going to post a response to Daywolf and Saludeen, addressing points one by one, but I just don't have time. I am getting a new postdoc in the lab next week, just got a new PhD student, and am trying to hire a research assistant. Instead, enjoy this fun video of a 2D representation of space(time) as a tool to understand orbits.
https://www.youtube.com/watch?v=MTY1Kje0yLg I used to wonder some time ago why planets orbited primarily in one direction... this video actually shows it... fun stuff, you can learn a lot from playing with physics analogies.
However, there are lots of questions and comments in this thread that are very difficult to answer/respond to unless people know a bit about quantum and general relativity already. It is tough to visualize 3D spacetime warping, so 2D does a good visual job. 3D vector spaces are challenging to visualize... took me until the middle of grad school to be able to see them in my head. The weirdest thing that comes out of general relativity is that the mass-energy is the source of the field, and the field is the source of the mass-energy... no analog I can think of anywhere else in science. Also, when you mathematically traverse the event horizon of a black hole, the time and position coordinates exchange places in all physics equations. I have no flipping idea what this means.
The other coolest thing I have been reading about recently is Erik Verlinde's theory of entropic gravity, basically that gravity is not a fundamental force, but just an entropic force.
I can't make long posts any more, sorry.