"I have it not" counted wrong. the literal translationay be awkward im English but it is grammatically correct.
No. That is sort of like using nach when you mean noch. Ich habe es nicht is I don't have it, while ich habe nicht es... is the beginning of a sentence. So something like ich habe nicht es gefunden would work in that way but in that case you're saying I have not found it... but the emphasis is on the it very specifically.
Practice. Seriously. You just become familiar with the syntax after a while.
Doesn't 'ich habe nicht es' mean more something like 'it's not the thing I have'?
Stand alone? Kinda. I mean, that's not really something you'd hear. I think if you really stressed "es" in there you could imply that.
It depends what you're saying. I don't have it = Ich hab's nicht (Ich habe es nicht). If you're negating, in a simple sentence, you'll see the negation come after whatever is being negated.
Where exactly does 'nicht' go in the sentence? Here I see it goes after the personal pronoun, but I reckon it doesn't always work that way.