Why am I getting this feeling that the case you refer to is
your own rather than your friend's? Too many similarities!! Coincidence?
Anyways, coming to the issues at hand:
1. Depends. What is the child's age - same as your child's?
2. The detailed process (form, fees, where to send, etc.) for registration of a minor as a British citizen at an overseas diplomatic post should be enquired from at the local BHC. The process for applying a passport is explained in the link already provided to you above.
3. If an interview is necessary then it is common sense that the parent(s) resident in UK may need to travel to the country where the passport application has been submitted. That said, if this child is the same age as your son (2.5 years), I have my doubts about the need to "interview" a 2.5 year old!