I know that some of them she learned by ear (pop songs she wanted to play). How unusual is this ability?
Learning by ear is somewhat unusual in the general population, but not that unusual in the musician population. Probably half the people I went to music school with couldn't read music (including some piano performance majors, though this subset was otherwise heavily slanted toward vocalists), and literally learned everything by listening. One of our DC learned quite a bit on an instrument without formal instruction simply from YouTube. There is lots of instructional material there, including dedicated piano tutorial channels.
Depending on what kind of music she wants to play on the piano, you might also consider interviewing teachers for their approach--e.g., classical, from the score, with a focus on finger technique; vs, pop/rock/jazz, from chords, with a focus on improvisatory technique. (Though neither, of course, should be entirely free of finger technique.) One of ours started lessons in a new instrument as an adolescent, after having attained a reasonably high skill level in another instrument, and has had good outcomes with a flexible teacher who generally is just a very laidback, kind, not condescending person. Critically, the formal teachers this DC has had were deeply appreciative of existing skills and musicality, and of DC's quickness in acquiring new skills. Consequently, they adapted their teaching to the student, rather than following a pre-planned curriculum strictly.
