I don't understand what you're asking. Are you asking if the fact that you are moving 10 m/s relative to, say, the earth, are the gravitons pulling you upwards? I think that is kind-of what you're asking.
The rubber sheet visualization is good for relativistic (i.e. large-scale) pictures. The particle/charge/gradient visualization is good for quantum (i.e. really small) pictures.
Since you asked about curvature, i think you mean space-time. Ok here we go (hehe uh-oh, mike's getting into physics again... run!!!!!) There's a few concepts we need to review first -
-If an object is moving at a constant velocity (no acceleration), the sum of outside forces on it is zero. Therefore, if an elevator is moving upward at 10 m/s and there is some sort of gravitational attraction trying to pull it down (the earth, for example) there is some force (the elevator cord) pulling it up.
This means if you are in a bubble in space and push off one end to try to speed yourself up, you will hit the other end with the same force and slow yourself down just as much as you had just sped yourself up. This is because there are no outside forces on the bubble (or there might be but they are equal).
-If an object is a certain distance from the center of mass (and so the center of gravity) of another object, it has a certain potential energy called Gravitational Potential Energy (or GPE), which is expressed in joules (J). It is transferred into kinetic energy if the object begins to fall (accelerate) towards the other object.
You can't use gravitons in the relativistic visualization of a curve in space-time. We use waves for those. In a quantum view, gravitons are exchanged and when they are, ***I am not sure about this,*** but maybe they would "pull" the other mass toward them by transferring gravitational energy. Or maybe they would attrat each other through gravitons through some sort of gravitational "charge." Anyways, the point I am making is that we don't even know if gravitons exist and so we don't know exactly how they work so it is all speculation.
Anything with produces gravitons. Well, they don't produce them actually. Since there is a conservation of mass in the universe, there is a set number of gravitons corresponding to the amount of mass in the universe (And on a side note, since you can convert mass to energy and energy to mass, maybe you could then convert gravitons to photons or gravitons to photons which might be one way to detect gravitons...). It follow then that gravitons are not produced by two gravitationally interacting bodies - they are exchanged.
I hope i adequately answered some of your questions, I did succeed in confusing meself, though! hehe oh well it's my 18th b-day today and I'm off to go lazertagging with my friends. Have a nice day!