child living abroad

My child traveled abroad while applied for british passport but due to emergency we traveled with back home passport. Now she has received her British passport can she come back on births passport?

Second she is living with her mother at the moment is not willing to travel within a year or so, what if her British passport expires in mean time. can she apply for it from there to renew her passport?

Child’s British passport is normally valid for five years.
Extend if expired.
Show both passports at airline’s check-in. Use British passport to enter the UK.