I don't know if I would make it an impossible timeline, necessarily, but definitely one that was extremely convenient for me, work-wise, regardless of whether it was convenient for her.
But part of the OP's problem is that she's asking ill-timed questions that she should be directing to her manager, not him. Questions that he can't answer much of the time anyway. If he wants to put and end to the questions she shouldn't be asking him, then a near-impossible timeline means he is a dead end to her, so she'll (hopefully) stop asking altogether.
If it was asking relevant quesitons that he could answer, and it would be appropriate for him to do so, then he can set a time for her that works. But "Do you think the manager hates me?" is probably not a question he needs to bother himself with ever.
I see your point, but I was thinking of a situation where the OP says, "I'm busy now, but I promise I'll answer that for you at 6pm," while knowing full well that the OP intends to leave work at 5pm and not
answer the question. In other words, I don't think that I would lie, or tell the employee something that would be recognized as impossible or ridiculous to someone else in the company--the OP seems concerned with appearing to be helpful to the employee, not getting in trouble for being un
helpful, etc.. If the employee started complaining that the OP promised to help her "next week," but the OP was then out on a pre-planned vacation all next week, or something like that, it wouldn't look very good for the OP, and I don't think it would teach the employee anything, except that she shouldn't be put off by the OP's excuses/promises, because they aren't real. It might make her even more
persistent. Maybe I'm just being too literal.
For legit work-related questions, I prefer the idea of giving a reasonable timeline that the OP intends to follow through on, like, "I'm busy now, but email me your questions and I'll look over them before the end of the day." If the employee does this, the OP could easily reply to that email something like, "I looked over your questions and realized they should actually be answered by your manager, so I'm CCing him on this. Hopefully he can set you straight. See you tomorrow!" if the questions are indeed of that sort.
For personal, chatty questions, I think the OP could use one of the methods others have mentioned to shut the employee down--"I'm busy right now and don't have time to chat," or something.