How can <PERSON> pilot a TARDIS? [Spoilers]
<PERSON> pilot a TARDIS
! with <PERSON>, in the end of Hell Bent.
But, except for short or emergency flights, normally with the presence of the Doctor alongside, no human (River Song isn't pure human) would have been able to pilot the Doctor's TARDIS by themselves. There are many difficulties with the way it's portrayed:
1. <PERSON> is shown reading the manual, which is written in Gallifreyan, arguably one of the most complex and difficult languages to learn and understand in the universe. I'd imagine a cross of Chinese with Category Theory (in math) might be similar to nursery level in Gallifreyan. Not only the language is difficult, many of the concepts probably don't even exist in human language.
2. Piloting the TARDIS (safely, at least) should depend on an extensive knowledge of temporal mechanics which would have been beyond the capabilities of a human brain, no matter how long they'd have to study it. The Doctor was seen trying to teach <PERSON> how to pilot the TARDIS, yes, but the "safely" is still open for discussion. The TARDIS can destroy the Universe in case something wrong happens (see Big Bang).
3. 837
Being human, both lack the Time Lord temporal senses, which may have something to do with piloting the TARDIS as well. Like having eyes to be able to fly a plane.
4. Most crucially, I think, as <PERSON> they'd lack the symbiotic nuclei, which AFAIK are necessary to establish the symbiotic bond between the TARDIS and its pilot (I believe it's said in PROSE: Interference - Book One).
The TARDIS will die if its pilot dies, so it's not like someone can simply take over a TARDIS. They need their pilot. River Song has been modified by the Silence with many Time Lord characteristics, including the symbiotic nuclei which are also necessary for the regeneration, besides having a connection to the Vortex from the moment of her conception. Even so, she needed the Doctor's TARDIS teaching her. How did <PERSON> and <PERSON> manage it, with a bog-standard TARDIS which wouldn't be accostumed with non-Time Lord passengers, let alone a non-Time Lord pilot?
Another point is that with all the trouble the Doctor finds traveling in the TARDIS, having a pair of humans flying around with a TARDIS of their own is a serious risk of universe-destroying paradox. For example if <PERSON> manages to get "killed" along the way, with no Doctor to save them. Remember the Doctor deactivated <PERSON>'s Vortex manipulator for this reason, and <PERSON> was a trained, and experienced, Time Agent. 837