Option 1: hope -> Incomplete response; needs "so" or "not" to be grammatically complete.
Option 2: hope it -> Incomplete and grammatically incorrect; cannot stand alone as a response.
Option 3: hope not -> Complete and grammatically correct; standard way to express negative hope.
Option 4: don't hope -> While non-standard, can be used colloquially to express lack of expectation.
Hence, Option 3: "I hope not" and Option 4: "I don't hope" -> When responding to a question about whether something will happen, "I hope not" is the standard, grammatically correct way to express that you hope it won't rain. "I don't hope" is less common and considered non-standard, but may be accepted in informal contexts to convey a similar meaning -> correct