Is gravity a vector or tensor function and does gravity have velocity or is it instantaneous? If gravity exists quantumly it must take up space, have frequency, velocity, etc. Perhaps gravity is too fine a frquency for detection.
 A: According to general relativity, gravity is an apparent effect of the distortion of space-time.
Both quantum field theory and general relativity describe some of the properties you mentioned:


*

*In QFT it is possible to describe particles known as gravitons that mediate gravity

*In GR it is predicted that gravitational effects could spread in gravitational waves


There are some experiments being performed to detect gravitational waves through gravitational wave detectors. Although the experiments are very difficult due to the minuscule effects expected, the frequencies are not the problem.
A: Be careful (as the other two answers here are) to distinguish between the speed of DISTURBANCES in the gravitational field, and the 'speed of gravity'.  
The former is a well-posed, meaningful thing.  The latter is not--the Earth's gravitational field, for instance, is mostly static--we just feel the same ol' gravity all the time.  So us Earthlings talking about the 'speed' of Earth's gravity doesn't mean much.  Now if a black hole hit the sun, and we started noticing changes in our gravitational field, we'd be able to talk about how quickly the gravitational news of that collision reached us.
A: The speed of gravitational interactions is well-known, in the classical GR context, but must be the same in a quantum theory of gravity. This speed is c, the speed of light. The hypotethical particle of gravitational interaction is called graviton. It is a massless particle (so it can go at the speed of light) and it should have integer spin (as all bossons, which carries forces).
A: As for the first question: gravitation is a tensor interaction of rank 2 (for more advanced readers: traceless metric transforms under the (1,1) representation of the Lorentz group. On quantum level this gives spin 2 particles called gravitons). This is really the same thing as with electromagnetism. There you have a vector interaction because field potential $A_{\mu}$ is a vector. (and the same comments can be made about Lorentz group and spin; in particular, photons are spin 1 particles).
It's not really correct to ask for velocity of gravitation and two distinct things can be meant by this:


*

*the speed of expansion of universe: this can be a lot larger than a speed of light. For more on this see any book on cosmology (or google) and expansion (in particular inflation).

*the speed of gravitational waves, i.e. disturbances in the background metric. These waves propagate at the speed of light.


Now your questions are actually interesting when asked together. Because the answer to the second one (propagation of waves at the speed of light) means that the corresponding particles are massless and this implies that they have number of degrees of freedom smaller by one than what you would originally expect, because longitudinal modes aren't allowed for massless particles. E.g. with electromagnetism, this corresponds to the fact that you get only two polarizations (right- and left-moving).
A: Gravity is an occurrence when there is mass/energy along the space time continuum, it is a forces, thus would be considered a vector as objects with mass are bound by a larger object's acceleration.
