can חי also be used as a noun meaning "it's life"? or is that only with the word "חיים"
Imho I suppose it'd be correct, but it wouldn't be as good of a translation because "this lives" isn't as commonly used as "it's alive" and therefore sounds awkward.
"It's alive!" is a quote from a movie, "Young Frankenstein", with Gene Wilder. So, while "this lives" may connote the same thing, it wouldn't resonate the same with those who know the movie. See Mazzorano, above.
Aware of this. But it should be an acceptable translation, because it's correct and there are situations (albeit few) where you would use it. For instance, you forget to water your plants, they shrivel up and die, but as you get rid of them you discover one green sappling. "Hey," you say, "this lives!"