Are cops allowed to handcuff a 11 year old boy that is not fighting against them?

More details are needed... if the boy had a gun, sure they could.

They may handcuff a 13 year old if they are talking him into custody for any criminal violation.

In fact many police departmetns have strict rules that anyone being transported or detained for a criminal offense be hand cuffed for not only the officers protection, but also for the child or persons safety.

A 13 year old can be very dangerous and merely being a child is no special meaning except how they are treated in court