Apple TV connection
see above: how can I connect my iPhone running on network A (wireless) with appletv running on network B (cable)?
That wouldn’t be an issue if both the wireless and the wired are controlled by the same router, then it is easy (or even default) to have the two parts bridged as one logical network. That is how I have it in my home.
With multiple routers and/or access points and/or nodes, one router would be the main, and the others should connect in bridge mode to have them extend the existing network.