You're trying to mix two theories. If you want to consider that photons are deflected by gravity, then you must consider that mass is energy.
By Einstein's special theory of relativity, the energy and relativistic mass of a body are related by $E=mc^2$. This works both ways. A massive body has energy, and a body with energy has mass. A photon has energy $h\nu$, so it has (relativistic) mass $\frac{h\nu}{c^2}$. Note that it still has 0 rest mass--rest mass is $\frac{E\sqrt{1-v^2/c^2}}{c^2}$. It will be deflected by gravity, but only a tiny bit (due to its tiny mass). And no, in General Relativity, acceleration due to gravity is not independent of mass as Galileo thought.
In General relativity, gravity works by not exactly being a force, but more of a distortion of spacetime. Spacetime is distorted such that what you feel is straight is curved from someone else's point of view. So an astronaut in the ISS can reason that the ISS is going straight (as long as he doesn't look at the stars or at the ground), as he feels no force (this is not due to small value of g, any orbiting body feels no force, even classically). You, on the other hand, are standing on the ground, and you say that it is going in circles. This is due to the distortion of space. (I can clarify this with the rubber-sheet analogy if you wish)