Okay, so I figured out the mechanics behind it.
Yes, you can play against your own ghost.
In order to save a ghost, you need to be ranked Beginner E or above. Your records will then start being saved under your personal info.
If you manage to score -1 or better on any course, a ghost should be saved.
However, that's where bugs and glitches might prevent/corrupt ghost data's accuracy, and sometimes may not save at all.
But that's just a little discovery I made for you to digest.