Can חוץ לארץ be used to mean "abroad" generally, or only in reference to Israel? If it's only in reference to Israel, how would you say "abroad" in general?
Originally only in reference to Israel, but nowadays it just means abroad. (And the more common way to use it is with an abbreviation, חו"ל).
Is the abbreviation just in writing, or is it also pronounced "khul"?
It's also pronounced khul.
Why is incorrect לחוץ alone?
Because חוץ doesn't mean abroad. חוץ by itself doesn't work here, it's meaningless in this context.