Do not be intimidated by the json file.
A json file typically contains data (in this case, configuration settings) in a separate file (like a text document), stored in a server's directory (like your local disk>documents folder, or whatever location you choose to save it in).
A website (in this case, the wab app) is served out to the world wide web with a web server (Apache, IIS, etc).
At some point, the website calls a json file to display the data the json file contains in the website.
In this case, the app's json file will contain the configurations you made in the configurator.
It will not hurt anything to look and become familiar with the json file.
You will see it is easy to work with, because it has the same settings you configured in the app's ui side.
My suggestion was so that you wouldn't have to spend a lot of time configuring the query widget in the ui side, since all the configs are listed in the json already.
I'm not sure what you mean by:
"We host the app on our own server, but so far, all changes have been made on AGOL."
If you are serving the app from your own web server, you will not be able to configure in agol (as far as I know).
Do you mean that you are hosting the services from ArcGIS Server, but then using your services in an agol web map, then making an agol web mapping application from that web map?
I'm not sure how to answer:
"If I have to download the app to put onto the server, and no changes have been made, why would the Query Widget suddenly become corrupt?"