1) No, substances almost never completely absorb photons. Otherwise you could not see them. In case a substance would absorb all photons (which is quite hard to achive intentionally) it would be pitch black even if you shine arbitrarily strong light on it (-> black-body).
2) It will be reflected back and forth, but only a finite amount of time. This is because reflectivity (or, equivalently, the probaility of a photon being not absorbed) is not 100%. Mathematically and experimentally one observes an exponential decay. (-> integrating speheres).
Example: Integrating spheres are hollow spheres and made of very high reflective material and have one small opening. When you look into the opening it will appear white. When you shine light into the sphere and turn it off suddenly, you will observe that it takes some time until the light has completely decayed. This is because the photons which are stored inside it, are reflected back and forth in it until they have escaped or are absorbed by the non perfeclty reflecting material. However, even for very high reflectivity spheres this time is typically below a microsecond, so you cannot see this effect with the naked eye. It is well measurable though, and basically the ring down time is so short because the speed of light is so high (and you have many many roundtrips in a time interval).
3) They will be reflected (and with higher probability than photons of other wavelength, otherwise it would not appear blue).