iMac G4

That is because the OS is too old to support newer versions of mainstream browsers and web pages. A firm that issues security certificates to web site owners allowed allowed older certs to expire on 30 Sept leaving many users of older computers stuck. Basically the replacement of the lapsed cert needs macOS 10.12 Sierra or higher, an OS unavailable to the G4 iMac.

You can try downloading TenFourFox. It is a fork of FireFox made to run on PowerPC Macs. Modern web sites see it as a supported version of FireFox. I use it on an G4 eMac running OS 10.5 Leopard and have received no cert errors. Development and support of TenFourFox has stopped but it can still be downloaded and used:

http://www.floodgap.com/software/tenfourfox/

Note that this is not a perfect workaround. TenFour Fox does not support video plug-ins so stick to more basic web pages.

WiFi and LAN-"wire" are two totally different things.

I'm assuming your WiFi "tower" is the router that was supplied to you by your Internet provider. They usually have ports in the back to plug in LAN computers, as well as offering WiFi capabilities as well.

You should be able to plug a LAN cable from your iMac to the back of your router with zero issues and it should be automatic. If you do not want to physically plug your iMac to your router, you just need the SSID (Network) and Password which is usually written on the bottom of the router.