Sounds like you control both a-page and b-page.Personally, I would not have Launch in b-page at all. Instead, anything that needs to be tracked should use window.postMessage() to send messages to a-page. Then, configure Launch in a-page to listen for those messages, then track accordingly.I had a similar setup where b-page showed a video and I wanted to track those video interactions. So with every video interaction, I used window.postMessage() to send information about that interaction to my a-...

It will be difficult to provide the exact implementation details because it depends on how the internal search function has been built into your site.But basically, when the search results are shown, you should then update your data layer with the search term and number of search results. Those should be populated by your internal search function somehow. After your data layer has been updated with them, then you can track as desired to your analytics tool.

Yes, your assumptions are correct.In general, Custom Code actions are loaded via separate JS files. So you will face a race condition in Scenario 1 where the browser is loading that JS file for your action, but then the browser also redirects to the next page.

If the Customer ID is set in a cookie or session/local storage in the user's browser, then you can create a data element of that storage type, and track it in your tags.