IF you don't mind her contacting you on facebook, you could send her a very short FB message and answer some of her questions, just so she gets a response (the reward for leaving you alone for two weeks). But at the same time, you'll be modeling the desired behavior of keeping non-work-related topics in a non-work setting (facebook). And you're not helping her to get through her WORK day...you're keeping the personal chat for personal time.
How about something like:
I saw your message that you sent me at work, so I wanted to get back to you when I wasn't working. Cars are fixed, thank goodness! Glad you had a nice holiday weekend. School will be done soon, so that will be a relief.
One of my FB friends got a bug up her behind for a while where she'd have a question for me, and she'd post it on my wall rather than send me a message. Geez, if you have a specific question, put it in a message, not on my wall! So I'd delete it from my wall and respond to her in a FB message (which is where IMO, it should have been in the first place). She hasn't tried lately, so hopefully she got the hint.