When I set a master page and apply it to the child pages, does it ignore the styles of other pages and apply the styles defined in the master page? As a result, the other pages appear with a broken style. Where am I going wrong?
I think that is the usual behaviour because the Master Page is the full page template that you are using and it would overwrite those child pages.
If your other pages are appearing with broken style, that’s a bit unusual.
Try to create a new page and use the Master Page as a template. If you are not getting broken styles, then the issue is with those child pages. If you are getting broken styles, it might be with your css/js etc, check their paths.
The other way around this is to use Components, and just apply them for what you need menu, footer etc.