In addition to the other answers, I would add "have" in the sentence. "I have never left the library, not even for one day." If you'd prefer to not use that word, I would change "left" to "leave". "I never leave the library, not even for one day." As others have said, this is a bit strange sounding as you are effectively saying you literally live in the library and do not leave. "I never skip going to the library each day" or "I have never skipped going to the library every day" may better convey what you're trying to say.

Your sentence does not mean what you want it to mean. "Left" is the past participle of "to leave". "Leaving the library" means exiting the library. Here are some ways to say what you want: "I never skipped (or 'missed') a (single) day... ...at (or 'in') the library" ...of library study" ...(of) going to (or 'studying in') the library" ...of study at (or 'in') the library" ...studying at (or 'in') the library" Alternatively, "Never did I skip (or 'miss') a (single) day... "Never have I skipped (or 'missed') a (single) day... ... (same choices as above)

It's okay. Could be better. With phrases that include "never...even" you could add "not" as this adds more stress, and it's common to do this when speaking. "I never left the library, not even for one day." Technically it's a bit strange that someone would never leave the library. I mean they probably would go somewhere else to eat and sleep, etc. I imagine that you intend it to be a bit of an exaggeration and not to be taken literally? You could of course use the verb "skip" as you have in your question. "Consulting the library" is also quite formal. I think people are more likely to say "going to/using/visiting/studying in".