The director of my area assigned someone to monitor me. She went to ask everyone I interact with what I do. She tells me to report everything I do every day, even controlling where I sit, and it makes me wonder if I will be fired. What should I do?
It certainly sounds like you are being set up to be fired, but you could spin this another way.
What's another reason someone might be put in to observe your work?
I say you take on that they are observing your work because you are an exemplary employee, efficient, producing amazing results, and they want to study what works here in order to reproduce it. Of course this works best if you do actually bring a strong work ethic, a commitment to excellence, and ownership of the job and your company to your work (If you don't, it's time to start).
Then declare yourself this observer's partner, offer to create the manual for what you do, get (more) curious about how your work affects the health of the company and the value you add, and look with her at what can be done to take that up a notch, to make things work more smoothly with your colleagues, to improve channels of communications and optimize channels of production.
Talk to this person about goal setting for your job and making sure you are focusing on what is most important. Set goals, communicate them well, and exceed them.
In other words, be friggin' amazing. Add value to every interaction
But if the seating bothers you, this is a place you can take a stand. On the other hand, if it's just another slight to your dignity, then personalize and make the new spot beautiful and thank her for the new work space.
Now, if you get fired anyway, you've left a door open behind you that you can always walk back in to for a recommendation, or that you may be invited back into if they really see that you are the best for your job.
And if you don't, take on this way of being for the rest of your working career.
And, if this all sounds way too far fetched, then ask yourself if you were really that into your job anyway, and weren't just setting yourself up to be fired anyway. It doesn't matter that others might occur to be less into their job and even less value to the organization. (This is not for you to judge.) They might smile differently at the boss, actually have better results, or just not be as annoying as you are.