The easiest question first: yes, you do need to have a Grade 6 theory pass before entering, but check the syllabus for alternative qualifications which are acceptable.
As for your other questions, it really depends how much teaching experience you have. I took the DipABRSM in flute teaching last year with very little preparation for the exam itself, but I had been teaching for seven years prior to that and had a great deal of knowledge of flute repertoire for different levels of player (although not for the imaginary 14-year-old boy I was asked about in the exam, as I've only ever taught two boys and both were 18!).
If you've not done much teaching, I would see if you can find a Grade 6 guinea pig to try out your three pieces with, and talk to other flute teachers about some of the main issues that arise in their teaching.
Good luck!