I would also like answers to these questions

Best counterexample would be peregrines and eagles. Comparatively small eyes but perfect vision at great distances.

There is a physical limit to seeing things with just light. IIRC, atoms themselves cannot be seen with light unless there’s a large molecule of them. They use electrons to see them.

When you say “vision” you are probably meaning like-human vision. My understanding is that a lot of smaller animals rely more on smell and taste, than sight. Although flies can see fairly well close up. But, in terms of “smallness”, I don’t think most animals can detect microscopic organisms with sight but perhaps with other senses.

Ants have rather poor vision compared to humans, but mostly a completely different vision:

Like most insects, ants have compound eyes made from numerous tiny lenses attached together. Ant eyes are good for acute movement detection, but do not offer a high resolution image. They also have three small ocelli (simple eyes) on the top of the head that detect light levels and polarization.[39] Compared to vertebrates, ants tend to have blurrier eyesight, particularly in smaller species,[40] and a few subterranean taxa are completely blind.[2] However, some ants, such as Australia’s bulldog ant, have excellent vision and are capable of discriminating the distance and size of objects moving nearly a meter away.[41]

https://en.wikipedia.org/wiki/Ant#Head

Generally, larger eyes (in absolute terms, not relative to the individual’s body size) are likely advantageous for high-resolution vision. A larger eye can have more photoreceptors, and a larger pupil can take in more photons. Both factors increase the amount of information available for the brain to construct a detailed image.

Optical vision encounters physical limits when the detail size of observed objects becomes smaller than the wavelength of light being used (see “diffraction limit” or “Rayleigh criterion”).