I cannot or I do not see/hear/feel etc. mean the same thing in English. We do not know why but we know you cannot/do not. In Czech it is simple vidím-nevidím.
When you engage MOCI in Czech it starts having slightly different meaning and you would likely use "able to" in English. Já to nemůžu vidět = I am not able to look at it/watch it
I am a native English speaker, and in English I cannot and I do not see/hear etc. are very different things. "I cannot see the dog" means "I am not able to see the dog" either because, for instance, something is obstructing my view or because I am blind. "I cannot" should not be an accepted translation here.
As a native Czech I can tell you that many times whenEnglish eant to stress they are not able to see something we say "nevidím" anyway. For the purposes of translations from and to Czech "see" and "can see" should almost always be translated the same way.
Can you see the little ducks?
Vidíte ty malé kachny?
Any other translation than just "vidíte" would be extremely unnatural.
If you're talking about accusative case (sing.) of "ten", then yes, it only works for animate nouns — Mám toho psa. Nesnáším toho kluka. The inanimate masculine nouns (+ adjectives and pronouns) stay the same as nom. — Mám ten velký stůl.
But you need to remember that "toho" is also genetive case of "ten" (both animate and inanimate masculine nouns) and even "to" (neutral nouns).