How do you understand the sentence "Switching to Free Running mode (ADTS[2:0]=0) will not cause a trigger event, even if the ADC Interrupt Flag is set." on page 266 ?
Means that you have to start sampling by yourself, in case your trigger (on this scenario, the ADC own "sampling end" signal) does not come after you enable the free running mode.
Figure 23-7 on page 255 really shows only 13 cycles per conversion on Free running mode so Free running might not be related with auto-triggering since no trigger event will be generated !
I'll reply soon to this. I'll explain some stuff in detail, like why 962 samples, how timebase is computed, how dual-channel works and how can it work otherwise, why only 16 prescaler for now. Cause now I'm sleepy. 
Best regards,
Álvaro