Can a bathroom fan be mounted on one of the interior walls instead of the ceiling?
You can install a wall mount fan in a bathroom and meet code in all places I have done work.  I have used them a few times (going straight out an exterior wall).  In cold regions I would never go straight out because of the backdraft but since you are on an interior wall its not a big issue.

Now if your city needs to pass this I would call your inspector and make sure what they want out of this.  Every inspector I have had wants these within a foot of the ceiling - so if you aren't needing to pass inspection use that guideline.  I am not sure where that is written in any building code (please add it if anyone can find it) but I have gotten that answer in a few places.  Here is an example of a fan you can use.

Note that using a wall mount isn't as efficient as a ceiling mount for the obvious reasons, the warm moist air can rise above your wall mount opening.  But if it is impossible or very hard to go ceiling mount they work.