1) One such term, a little old-fashioned maybe, is "worrywart."
When a person is imagining terrible scenarios that might not ever take place ("What if he misses his plane, then he'll be stuck in Philadephia overnight and if he can't find an ATM then he won't be able to eat...") we also say he or she is "borrowing trouble."
2) "She worries about nothing" grammatically can have the first meaning you list, but I would use it more commonly to mean the second. I would probably emphasize the word "nothing," when I spoke to make the meaning clear. I know I hear, "You get yourself all worked up over nothing!" often -- probably because I am a "worrywart."
[native speaker, not a teacher]
Student or Learner