"It is not short."
In Japanese, the subject (the person/thing performing the verb) is often left unspoken, and only understood from context. The sentence above doesn't actually contain a Japanese word for "I" or even for "it" - basically all it literally says is "is/are not short," which sounds incomplete in English but is pretty normal in Japanese. "It" is used in the translation because English demands a subject, and it's pretty much the closest you can get to the implied, context-dependent subject in Japanese.
みじかい is not used to refer to people's height in Japanese. You'd use 背が低い (せがひくい) to refer to a person as short instead.
What's the difference between みじかい and みじかく? Is it the fact that one is a negative sentence?
I think it's the adverb form by adding -ku, which is, again from what I've gathered, is required when constructing the negative with -nai.