Can I use a home plug to amplify FREE WiFi?

This sounds like a system I installed in a local a small hotel, inn and restaurant. Place was a 19th century stone built building, which was fairly narrow but was considerably further from front to back.

The landlord and family have had an apartment at the front over the public bar, which took up the front part of the building. Behind the bar were the kitchens and a corridor that lead to the restaurant at the back of the building.

The building had a single ISP feed that went to a wireless router at the front end of the corridor that lead from the landlord's apartment to serve the six guest bedrooms that ran back over the kitchens and the restaurant. From that router an Ethernet cable went into the apartment where there was another router providing a separate subnet for the landlord and the hotel's administration. This second router blocked access to the hotel systems by any guests or people in the bar.

I used Powerline networking (Home-plug) to provide service to the guest rooms at the opposite of the upper floor corridor, and also to the pubic bar. Both these used a Powerline adapter with WiFi access points built in. The four WiFi networks (landlords, the two ends of the bedroom corridor and the bar) all used different network names. The landlords network was hidden and was WPA2 protected. The guest and bar networks were unencrypted.

The main ISP router used channel 1, the access point in the bar that was the closest used channel 11 and the landlord's router and the access point at the opposite end of the corridor used channel 6.

I used separate SSIDs to prevent devices hopping from one WiFi source to another as I have experienced on some sites I have visited. Although many people talk about devices connecting to the strongest network when there are several with the same name, since WiFi does not produce a continuous transmission, the strongest signal may not actually be transmitting when the user's device is scanning.

Coverage was aimed at the apartment, guest bedrooms and the bar, but to exclude the restaurant.

I implemented this in 2009 and continued to support the landlord with his network for about 4 to 5 years before I had to retire from my support role due to illness.

Yes, but that isn't the best method! Adding another ACCESS POINT to the system is the best solution. AP's can be added anywhere are are directly connected to the router so you don't loose 30-40% speed! A repeater (like homeplug) will loose speed for each device as it has to receive then transmit to the main AP then receive from the main AP and transmit back to the "client" so it slows the system. But yes it will work.

you can use a variety of PowerLine adapters thus utilising the wires of your buildings mains connections. Alternatively you can daisy chain two routers together where a 2nd router is connected to the 1st using a lan cable, and then you can locate it upstairs, only needs the length of a cable and a hole in the ceiling/floor. lan cables can go up to 500metres. the 2nd router has to be a cable style router usually easy to identify as being with 5 lan ports where one is colour coded and labelled as WAN port(input from 1st router). the 2nd router would have its own wifi signal. Many people throw away their old cable tv style routers when they are ideal for becoming 2nd routers as they dont have a modem which sounds a bit like the one you have already. They offer internet passthrought and very little configuration as thats done by your current modem. they just need a different starting IP ie main router might be 192.168.1.XXX and 2nd router would be 192.168.2.XXX and would then refer back to the gateway of the 1st, usually 192.168.1.1

it would be better to use a wifi extender

it would be better to use a wifi extender. HomePlugs cause problems with electrical stuff in the same building.

No, you would not be able to use an extension plug, as you would need the password or access to the Router. You will have to drink downstairs and get the stronger signal.

Wtf is a home plug?