I don’t see any reason for the application to be refused but if it were, would the fact that she’s a British citizen mean I would stay on the 10 year route? Or would they kick me out regardless because she’s so young? I’ve read simply having a British child puts you on the 10 year route, but I don’t know for sure.
You are being asked all these questions due to all the abuse from too many who try to stay in the UK when they have no right to stay. These often enter the UK as an international student, can't find a work sponsor to reach ILR and they don't want to go home. They try to stay in the UK anyway they can and often they try to reach the 10 years of legal stay for ILR, by any means and the UK had/has to bring new rules or laws to stop/remove these.
If you tick all the boxes for the visa, you will get a visa. The reason for the details for any human rights, is for the HO staff to now look at this at the same time, if the applicant cannot have a visa to remain. Under the Immigration Act 2016, Human Rights appeals are now outside the UK, which is not what they want as they want to remain in the UK: and their human rights appeals (continued appeals until they exhaust all their appeal rights) will likely fail anyway.
This is just one of the many examples where the dishonest migrants always make it harder for the honest people.
I always thought an invalid application now not having protection of 3C of the Immigation Act 1971, due to the abuse, is one of the worst things for an honest migrant who made a careless mistake. Also the 28 days allowed if they forgot to renew their visa, that was also removed due to those who just didn't bother to renew on time (abused the spirit of that 28 days).