True HDR is done with bracketed shots, a minimum of 5 shots is recommended.However you can still get some interesting results out of one RAW file. It is worth experimenting with if that's all that you have to work with.
It is still true HDR by deriving multiple exposures from a single RAW and then combining them. You are just using the computer to bracket instead of the shutter. It often leads to better results as multiple shots often gives you minute movement in trees and clouds which leads to blur in the HDR final.
This is debatable depending on who you ask. FWIW, I agree with you but if you go into some of these HDR discussions, there are plenty of people who will say using one RAW file is not actually "high dynamic range" and you are just tone mapping. Technically they may be right, the only way to achieve true HDR is to get maximum values from the darkest and lightest parts and that's not possible in a single RAW file. But whatever the case, you can get results from a single RAW. You are correct about the blurring of moving objects and if you are handheld you can even get some camera movement in the bracketed shots so those are the advantages for using just one file. My experience has been that at least 5 bracketed shots produce the best range in your images, given that there is a large dynamic range to capture but this is not to say that using a single RAW is not acceptable. Also using a tripod is advisable to eliminate any movement of the camera and also to get more bracketed shots, my D80 maxes at 3 shots.