"at most one". As you get further away zero protons are reaching you on most cases, and zero photons times infinite stars is zero, which would appear to be darkness
Zero multiplied by infinity does not have to be zero, it can be anything between zero and infinity. Refresh your https://en.wikipedia.org/wiki/Calculus.
The discreteness is a distraction here. You are interested in the total flux of light, from all stars in some patch of the sky. If some of them contribute on average less than one photon, that doesn't matter, it doesn't cause some sudden drop-off in intensity.
If it did, the same thing would happen not just for stars, but for all sorts of things. If you position a computer screen on a hiltop far enough away that, on a dark night, you can just make out whether it's on or off, then your eyes are getting about 6 photons per second. It doesn't matter whether these come from a million separate pixels, or from one light-bulb of similar total brightness.