Is gravity a particle or a wave?
Your questions struck right at the center of one of the hottest and most challenging research topics in physics. So far, physicists don't know the full answers to all your questions. Although gravity is well understood at the macroscopic (every-day-life) scale, scientists are far from understanding it well at the microscopic scale (quantum level).
Gravity is a force. For all other forces that we are aware of (electromagnetic force, weak decay force, strong nuclear force) we have identified particles that transmit the forces at a quantum level. In quantum theory, each particle acts both as a particle AND a wave. This is called duality. So if there is a graviton, we expect it to behave both as particle and as a wave as well.
The electromagnetic force, for example, is transmitted by photons, and light is nothing but a large number of photons. Photons/light show wave and particle properties. (See http://www.fnal.gov/pub/inquiring/questions/light_dual.html for more information.)
Scientists expect that gravity functions in a similar way. However, physicists haven't yet observed a gravitational force carrier at the quantum level, and chances are they won't do any time soon. It takes very sophisticated experiments - much more sensitive and with much better resolution than we can build so far - to detect such a phenomenon. Nevertheless, scientists expect that a force-transmitting particle - the graviton - exists. Theorists, however, are still struggling to formulate a consistent gravitational quantum theory that incorporates a graviton and that correctly describes all well-known gravitational phenomena, including Einstein's theory of general relativity. The most promising attempt for a gravitational theory so far is based on Superstring Theories, and you can learn more about it at this Web site: http://www.superstringtheory.com
Before setting out to find such a thing as a graviton, scientists currently try to verify whether gravity produces classical (not quantum) waves, something that nobody has observed, but Einstein's theory of general relativity allow for such gravitational waves. The same way that you can study the wave phenomena of light without knowing about the existence of light particles (photons), one expects to be able to detect some sort of gravity waves without producing evidence for a graviton.
It takes huge massive objects, such as stars spinning around each other, to produce gravitational waves that might be strong enough to be detected on earth. There are a couple of experiments around the world dedicated to this search, one of them called LIGO. You can learn more about LIGO at http://www.ligo.caltech.edu/LIGO_web/about/brochure.html
I hope this gives you a little flavor of the exciting research going on with regard to gravity.
Kurt Riesselmann, Physicist
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