Firing rate of retinal ganglion cells
1) This is a bit simplified; in reality, flashes of light or dark that cover the whole receptive field do influence the firing rate somewhat, just not nearly as much as an on-center stimulus for an on-center RGC. Your textbook is using a bit of an idealized interpretation to convey the concept of center-surround organization. I'm not sure what your confusion related to the horizontal cells is, however.

2) This is usually called "adaptation" and is a general principle in nervous systems (particularly on the sensory side). Multiple systems influence adaptation, including depletion of neurotransmitter-containing vesicles, metabotropic receptors activated by high concentrations of neurotransmitter that have opposite-sign effects to ligand-gated receptors, feedback systems that suppress the potency of second-messenger systems, accumulation of extracellular inhibitory neurotransmitters, etc. For the eye, there are additional sources of adaptation that come into play, depending on the experimental paradigm.

Without knowing the exact paradigm your textbook is meaning to indicate, it's probably more important at this point to just recognize adaptation as a normal aspect of sensory processing. The specific mechanisms can be understood later.

3) Yes - but you don't need to go to anything as complex as an artificial neural network. Basic image filters like the Laplacian of Gaussian (LOG) filter are basic approximations of center-surround organization in the retina.