If as per Einstein gravity is the curvature of space near matter then how is it also composed of gravitons? Is gravity paradoxical at the quantum level like light being both wave and particle at the same time?
Einstein's relativity and quantum mechanics are mutually incompatible. One is a continuous field theory and the other is a discrete particle theory. One applies to the very large; the other applies to the very small. The Holy Grail of theoretical physics is to reconcile these two theories and there are some theories that attempt to, but so far, it has not happened.
Don't make the mistake of thinking that gravitons are part of established science. They are not. They are just a hypothetical idea, for which there is no observational evidence as yet. People think there ought to be gravitons to mediate gravity, by analogy with the particles that are said (in QFT) to mediate the other interactions in physics, e.g. the photon for the EM interaction. However when people try to do the maths, for what they think a graviton should look like, they run into hideous and currently insoluble problems. Something does not work. So either there are no gravitons and the whole idea is misconceived, or there has to be some as yet undiscovered feature of physics which one day may resolve the difficulties. Right now gravitons are just a dream.
I've realised my earlier reply does not address one crucial aspect of your question, namely why should we treat gravitation like the other interactions, when relativity tells us us gravitation is just the result of the geometry of spacetime - and not a "force" at all. I think that is a very good question - and I share your mystification. I imagine it has to be somehow to do with what it is about mass that causes it to bend spacetime. But I don't think anyone on this forum will be able to give a satisfactory answer to that, least of all me. The one man I know who could - though we might not understand the answer he gave - is called Markus Hanke, and he can be found on other science forums.
