DC motor voltage drop and high current draw
The reason your measured voltage drops significantly is the internal resistance of your battery. A 9V alkaline can't source much current, definitely not the 1.6A your motor would like. I'd be curious to know what you measure if you do the same test, substituting the 9V for 6 AAs.
Also, I'm sure your schematic is simplified, but are you using flyback diodes on your controller? Leaving them out leaves the L298 vulnerable to back emf from your motor. If not, it's probably burnt out already, which would explain some of the behavior you listed. Page 6 on your pdf has an example of the diodes.