I have been offered a job in another state, but I do not want to move there. I believe that I will be fired from my job if I don't comply. I have begun looking for other employment. In the mean time, would I be eligible for unemployement, or would I be denied because I did not move (the move is over 500 miles from my current location)?

If you are fired you won't be eliglble. You can appeal the decision but I'm sure the company will drum up some other reason for your dismissal.

No, a company can not require you to move further than a standard commute from your current location.
If they close before you quit, you should be laid off due to their closing that facility. You can not be fired for anything that is your fault, but if you are "fired" for not moving, you may have to appeal but should be able to get it.

If you want to be 100 percent sure, go to the employment security office and ask them face to face