Can gravity exist without mass?
Possibly. Gravity is a force that acts on mass, and is caused by mass, but there's no reason to assume that it exists only because of mass. If it affects photons and photons are mass-less then it stands to reasons that photons can also affect gravity equally. I guess then that if there are photons, there is probably gravity.
Though without mass, I have no idea where you're going to get photons from.
Also, assuming you could move mass in and out of the universe without violating the law of conservation of mass, then the gravity would be created as a ripple in spacetime, and even if you removed the mass after that, the gravity would not disappear - it would just go on propagating outwards forever, dissipating as it did. I guess it's a bit like throwing a rock in a pool. Sure, there's no ripples without the rock, but when it's gone, sunken to the bottom and no longer causing the ripples, the original ripples it caused continue outwards regardless.
No, the negative gravitational field of a particle is as much a part of the particle as it's positive inertial mass. The gravity field of bodies is due to their inertial property (But one must be careful as to what is meant by the word mass). Mass is not a separate thing from energy - but rather a state of energy. So a gravitational field can exist in proportion to the mass equivalent of a quantity of energy (e.g., spatial stress can be considered a mass ). A common example would be the increase in the gravity field of a mass engendered by the action of gravity acting upon gravity. In this sense, the gravitational energy contained in a gravitational field can be considered mass, and therefore the effective mass of a body is equal to its bare mass plus its gravitational mass (since this added gravity field is not due to the bare mass of the body, it is sometimes called mass deficit). While energy contained in the gravitational field of ordinary planets and stars is small compared to the mc^2 energy of the body, the gravity acting upon gravity factor becomes significant when the density of the body approaches that of a black hole.
Gravitational force, or spacetime curvature results from energy density and pressure, not mass, nor mass density. We could include a couple more but these can be eliminated by a change of coordinates. (I don't know why it became popular to confused mass with energy density.)
Now, light has no mass, but possessing energy and a density of energy, it is a source of gravitational curvature. If you want to see the mysterious equation for this, try "stress-energy tensor".
Wow. Deep question. Answer is YES. Per MC Physics, gravity force comes from electrostatic force between mono-charges. Mass comes from the electrostatic charge strength of those mono-charges, but the electrostatic charge still exists. Thus the 2 are directly related and depend on electrostatic charge, but gravity is more direct from electrostatic charge and does not need mass. More on that at:
Quite possibly. One big part of Quantum mechanics is the search for the subatomic particle that actually produces gravity. It may not exist, but it seems likely that it does. There are quite a few phenomena on the subatomic scale that clearly indicate that gravity does not exist on that scale, which implies that something causes gravity that is not absolutely linked to massive particles. Graviton is the colloquial name for this theoretical particle, you can perform more research into that if you're really interested in learning about the actual base cause of gravity.
Yes. Even if all fundamental particles were massless, we could still have gravity, because gravity originates from the density and flux of energy and momentum, which is only approximated by mass in the nonrelativistic limit.
(As an aside, even if all fundamental particles were massless, protons would still have mass, and, more generally, composite systems could still have mass. In fact, even in our current world, a box of photons still has a total mass. So really, one can't have "no mass," although you can have "no fundamental particle mass.")