Mesh will function about as well as an extender, so it's your choice. Placement is key so that the unit is still within good signal range of the main router, but also within range of where you need to get your signal to. It's a middle man. Mesh will function better overall as it will give you things like better roaming capabilities, etc. An extender is more like adding another AP, just cheaper and worst, so devices may stick to another AP before it switches to a stronger signal.
Powerline is complete garbage. It is very rare that it actually works well for people if all your cards fall perfectly in place. Wifi sucks, but powerline is worst. Always run a cable if you can. And if you can run a cable, then you can get mesh working at its best.
No, that would work. ISP to modem to router to switch. Switch to satellite mesh units and wall ports for devices.