Using a Raspberry Pi as a Wi-Fi Extender

Yes, it can be configured for access point or network-sharing roles, depending on the model and setup. It is not always a simple one-to-one replacement for a repeater.

The answer depends on the wireless mode supported by its hardware and software. An Ethernet-connected access point is generally a clearer configuration than assuming transparent wireless repeating.

Ethernet is not required for every design, but it provides a straightforward wired backhaul for an access point. A wireless relay needs compatible radio capabilities and careful configuration.

A Pi suits people comfortable managing Linux networking and updates. A consumer extender is usually easier when the goal is simply to improve household coverage.