I'll have to defer to someone like Willam van Weelden to say for certain. But generally speaking, my own experience with things like this is that whatever the attributes of the Master or Parent project are, determine the attributes presented from the child projects too. If perhaps a child project uses a different skin, that is overridden by the Master or Parent. That is, unless for some reason the child is opened on its own. Then you would see the child skin.
It's a while since I merged responsive help but I recall that it is different to webhelp and does change as you move from topics in one project to another. There's a simple merge demo on my site that you could use to test.
I will test this some time but cannot do so right now.
See www.grainge.org for RoboHelp and Authoring tips
Responsive help takes the skin from the master project (if you open the master project first). You don't need to duplicate per se. But it is safer to do so. Responsive HTML5 works the same as WebHelp.
Quick tip: cusomise the layout in the master project. Then export the layout. This will export the layout with all customisations. Simply import the skin into all child projects and you are good to go.
Note: This is only for RESPONSIVE HTML5. Multiscreen is a completely different story.
Thank you. So far, so good.