Is there experimental evidence that massless particles such as photons attract massive objects?

As far as I know there has been no experimental evidence that light curves spacetime. We know that if GR is correct it must do, and all the experiments we've done have (so far) confirmed the predictions made by GR, so it seems very likely that light does indeed curve spacetime.

The trouble is that spacetime is exceedingly hard to curve by any significant amount. Curving it is no problem if you have an astronomical body to hand, but measuring the curvature due to lab scale masses requires very fine measurements. Bearing in mind that mass is a very concentrated form of energy (by a factor of $c^2$) it's hard to see how we could ever get an intense enough source of light to create measurable curvature. There might be some indirect measurement possible, but none springs immediately to mind.

Yes, almost all of the mass-energy of ordinary matter is due to the gluonic field. Gluons are gauge bosons with zero mass (like photons). In the absence of gluons, the quarks making up protons and neutrons would have less than 2% of their usual mass. Since the measured gravitational interaction of matter includes the gluon-provided mass and is not just the quark-provided mass, we can be sure that gravitational interaction due to mass-energy does not discriminate between fundamentally massless and massive particles.

If you want to get back to photons, there is also a mass induced by the electromagnetic interaction. It makes protons a bit heavier than you would expect relative to neutrons. Again, there's every evidence that the gravitational interaction does not discriminate between mass induced by electromagnetism or any other source.

Of course, a beam of free photons is a bit different and requires more sophisticated calculation in relativity. Its very tiny gravitational interaction is impossible to measure using current technology.

The relationship between mass and curvature of spacetime is well-motivated, but not the consequence of some fundamental fact in GR.

There are plenty of experiments confirming the curvature of spacetime by masses, like gravitational lensing, the proper prediction of the perihelion of mercury, redshift in a gravitational field...

$E = mc^2$ is one of the most famous equations in physics, but also the single most one quoted out of context. The full equation reads

$$ E^2 = \vec p^2 c^2 + m^2 c^4$$

This implies that indeed, mass is just a form of energy and the other way round that there is no fundamental distinction (in GR) between objects with energy from rest mass or energy from momentum. This can be seen by the fact that photons DO interact with the gravitational field (see gravitational lensing), wile their rest mass $m = 0$.