Yii2 testing environment guidelines for extension development

I am developing an Yii 2 public (MIT) extension to change some of the yii\web\View behaviours (minify, combine and many other optimizations).

I can do it easily. But I really want to write as many tests (codeception) as possible for it. This is where I am very confused.

I already have some unit tests (for example: testing a specific minifing, or returning combined minified result). But I would like to test the entire result and the final integration between my extension and the Yii2 web application using it.

I just would like some guidelines for this process:

1. Should I have a real (complete) app inside my extension for testing purposes? If so, should it be 'installed' inside tests dir?

2. Would you use functional testing ? (I think so because the View will find files in AssetBundles, combine and minify them, publish the result as a single file and replace the assets' urls by new url (i.e., the optimized asset url) inside the view;

3. Could you provide some very basic examples/guidelines?

I just would like to highlight that I dont intend you do my testing job, I really want to learn how to do it. This is why I really would be very grateful for any tips.

Thank you so much.