Can get a basic cat cable tester for pretty cheap: https://www.amazon.ca/dp/B01K1DBKN6 - this will cover basic connectivity & wire shorts, which is usually the issue. There are more expensive testers that cover more things.
You plug in each end and it sends a signal through each wire in turm, and watch on the other end to make sure it lights up in the right order.
The setup and setting in Google Home are really basic. Get the Google Wifi app and the network should just appear in there. It will give you a ton more setting and full stats on usage. You can also assign managers in here, which is great for managing the parents network remotely.
https://play.google.com/store/apps/details?id=com.google.android.apps.access.wifi.consumer