Hopefully, those members who claimed during their FLR period will provide some supporting comment for you.

There are some good postings here on the forum a quick search may help.

As a UK Citizen you can claim Child Benefits in your own name. You are entitled to it.

You may claim if you are responsible for a child. You do not need to be the parent of the child and you may be able to get Child Benefit even if the child does not live with you. Only one person can receive Child Benefit for a child.
Means stepchildren are included and can be claimed for.