Is there a way to keep hair childeren and edit the mesh? Editing a mesh after adding hair particles will mess up the hair (I assume it's because hairs are placed based on vertex order/indexes which change when the mesh is edited).

This can be avoided by disconnecting the hair from the mesh, but this will remove child particles.

Is there a way to keep hair (including child particles) in the same state while editing the mesh?
You could use a second mesh for the hair. This hair only object would sit just under the main object with the hair coming up through it.

This would allow you to alter the main object in any way you want without affecting the hair emitter.