To avoid confusion, there are no headphones in the mix.
Thanks for clarifying.
Seems you've basically grasped the concept. Your phone/tablet/computer will be for setup and control. There are desktop apps for MacOS and Windows computers and apps for both Android and iOS, which are quite nice .. not perfect .. but done well.
The only way you'll know if your WiFi signal is good enough is to try it and yes, it does matter. A WiFi extender or mesh router system can fix a WiFi issue if there is one.