Help with router Client mode!

Alright, here’s the situation... I'm dealing with a bit of a nightmare setup because running a cable from the upper floor down to the ground floor is basically impossible. The electrical circuits are completely isolated between floors, so Powerline adapters are totally out of the question—they won't work at all.
So, how does this Client mode actually behave? If I connect the device wirelessly to the upstairs Wi-Fi where the main router is sitting, am I able to plug other hardware directly into it via Ethernet—like an Android box or something similar?
Thanks for the help

"Client" mode works with Wi-Fi gear that plugs right into your PC via USB or a LAN port. Then you've got "AP" mode, which is for those Wi-Fi devices that hook up to your router using a LAN cable. Both Client and AP modes are basically just ways to stretch your Wi-Fi signal so it can actually reach more than one floor.
The thing is, we don't have any specifics on how many floors we're talking about here, what kind of router is sitting on that "upper floor," or why it's such an impossible task to run a 6mm UTP cable. If all the conduits running from the ground floor to the top are stuffed, couldn't we just run it through an unused chimney, maybe some ventilation, or even along an exterior wall?

Hey there... look, I'm dealing with one of those old-school stone houses—we're talking walls that are basically a foot thick. There is absolutely no way I can run a cable from the upper floor down to the main level. Up on the second floor, I've got this white Qualcomm router with white status lights. Downstairs, I’m working with a Netgear WRT2419... so, how do I actually make this work? Is there any way to configure that Netgear to pick up the signal and boost it for the bottom floor? Can I set that Netgear up to connect wirelessly to the main router?
Thanks for the help
Best,