Beings smaller than a proton? Science based?
Then I'm afraid the answer to any question you might ask about them is no.
Could they see the other protons?
A photon with high enough frequency that it would stand a chance of interacting with something so small would be far more than enough to send them flying at near the speed of light (assuming their mass is negligible compared to that of a proton). So, no.
Could they interfere with the supra-molecular world?
If they have such a small size and mass that they can live on a proton without weighing it down, then no.
And now for some questions you didn't ask, but maybe you should have:
Could they live on a proton?
No, protons aren't little solid spheres that have any kind of surface. They are quantum mechanical objects that can be here and there with no definitive boundaries.
What would they even be made of?
There's nothing even theoretically consistent with quantum field theory that could possibly allow for complex beings of that size. And you'd have to invent entire new sets of other forces and fields to account for it. Solidly in the realm of fantasy rather than science fiction.
Could they even know what they themselves are doing?
As Lio Elbammalf pointed out in a comment, due to Heisenberg's uncertainty principle, and due to how small they are, if they could know that they were in a particular place on a proton, they'd have no idea if they were coming or going or how fast. This isn't a matter of some problem with instrumentation or limited resolution of their eyes. It's an issue with the fundamental uncertainty of the things in this universe. When something's position is know to a significant enough degree, it doesn't even make any sense to say it has a particular momentum or vice versa.