No - in either case a https connection will be established and DNS will be available via that connection. The only exception is the very first connection of the browser/system, where the domain of the DoH provider needs to be resolved first (e.g. dns.quad9.net -> 9.9.9.9).
No, but check if the browser isn’t using other DoH provider. If so just disable it.
Note that it’s obviously a different story for mobile devices. If you connect to different networks, you might want to leave DoH on on your device
Makes sense, is their any downside if I set the same DNS in Android and Router?
No - in either case a https connection will be established and DNS will be available via that connection. The only exception is the very first connection of the browser/system, where the domain of the DoH provider needs to be resolved first (e.g. dns.quad9.net -> 9.9.9.9).