RPi 1 Model B as either a transparent wireless repeater or WiFi to Ethernet adapter?

[Master_W]

There are a few weak reception areas in my house that I'd like the wireless signal from my router to reach. I have an old router that would do just fine in AP mode, but the only option for running a cable from my main router would be to use a powerline adapter, which would be a little expensive.
Then the thought came to me that maybe I could use my RPi to connect to my main router wirelessly, and then share that connection over the Ethernet port to the AP. However, based on everything I've read, it's not possible to do this while having all devices be on the same network and getting their DHCP addresses from the main router. Everything I've read says that the Pi has to be setup with it's own DHCP server that would give different network IPs to any devices connected to the AP. While this would still allow devices on the AP to access the Internet, they wouldn't be able to connect to devices that are connected to the main router (such as my printer, Pi-Hole ad blocker, etc.), would they?

Another option I thought of was using the Pi with two WiFi adapters as a repeater. Is it possible to set it up so that all devices are on the same network and get their IPs from the main router?

To clarify, one of these two setups is what I'm after:

WiFi to Ethernet connecting to AP Method

rpi-wifi-to-ethernet.jpg (42.28 KiB) Viewed 1096 times

or

WiFi Repeater Method

rpi-wifi-repeater.jpg (36.42 KiB) Viewed 1096 times

Thanks!

[SurferTim]

I haven't tried this with a 1B, but it should work. It is a wifi-ethernet bridge.
https://github.com/SurferTim/documentat ... connection