Is gravity a factor for sustaining fusion? Does gravity affect a Fusion reactors ability to sustain a reaction? If so has there been any experiments done or planed for in space? 
Holding / maintaining shape might be a lot easier with less forces applied.  
 A: That's a great question, and it really depends on the type of fusion you are considering. Currently, the scientific community mostly works on two types of fusion - inertial confinement fusion and magnetic confinement fusion. I will mostly consider ICF as that is what I am working on.
In case of ICF the main problem lies in instabilities. Usually, a pellet of fuel is imploded by ablating the outer layer of a fuel capsule. As the outer material ablates, by the Newton's third law the centre of the fuel capsule is imploded and its density increases. It is in this phase that the denser fuel material inside is being imploded by a less dense outer material. Analogously to supernovaes, this leads to Rayleigh-Taylor instability that massively enhances any deviations from complete spherical symmetry of the fuel capsule and halts the fusion process.
In this sense gravity may be important - as it may slightly alter the shape of the fuel capsule away from spherical symmetry and lead to more pronounced instabilities. I believe I was even told once that it is taken into consideration during the design phase of the fuel capsules.
In magnetic confinement fusion I am fairly certain gravity is not an issue.
In gravitational confinement fusion (i.e. the Sun) gravity is the driving force that sustains fusion; however, this type of fusion is extremely inefficient in terms of energy generated per metre cubed of the reactor.
A: 
Does gravity affect a Fusion reactors ability to sustain a reaction?
  If so has there been any experiments done or planed for in space?

This was one of the very first considerations noted in toroidal experiments. I seem to recall Sakharov'searly paper mentioned it.
The gradient in pressure caused by gravity, small though it is in a plasma, causes a tiny asymmetry in the current flow through the plasma (because the density is higher at the bottom), and thus effects the stability of the plasma.
For really early designs this effect was too small to bother with. But by the 60s the Soviet toks were really starting to increase their densities and now it became a problem. This leads to the 1962 introduction of a new set of magnets above and below the chamber to create an offsetting field.
The good news is that this part of the field, while necessary, is tiny compared to the massive fields we're working with for basic containment. As a result, moving to space won't really help.
A: Gravity sustains fusion in stars by compressing the star’s gas to high density, pressure, and temperature. But gravity is negligible and irrelevant in any fusion reactors that humans build. Our reactors don’t have enough mass for the gravity of the fusion fuel to be significant. So we have to compress it in other ways, using magnetic fields, lasers, etc.
