1. The automated tests in my recipe project development pipeline would go within a Github action that runs whenever code is pushed because automated tests are often designed to verify recent changes to code have not broken any existing functionality. Running tests automatically on code pushed would allow for any problems or bugs to be caught early in the development stages of the application.

2. No, I would not use an E2E test to check whether or not a function is returning the correct output. E2E tests are used to automate test cases that simulate user actions. I would use a unit test instead to check for correct outputs of a function.

3. The difference between navigation and snapshot mode is that in the nav mode, it analyzes a page right after it loads and can analyze any interactions with the content on the page (overall performance). Snapshot mode however, cannot analyze these types of interactions or changes and only analyzes a page in its current state (mainly accessibility).

4. Three things you can improve are performance (speed-wise possibly through image rendering), accessibility, and improve the website's security as there are many possible attacks that could allow for possible attacks such as cross-site scripting, eavesdropping attacks and more.