Simply create a workspace project with the desired filters for page id's. Once done with the desired result, capture the JSON from workspace and use it in the APIs.Here is a video demonstrating the method of accessing the JSON for workspace: https://experienceleague.adobe.com/docs/analytics-learn/tutorials/apis/using-analysis-workspace-to-build-api-2-requests.html?lang=en#apis

It depends how the search keyword was passed on by the search engine. Search engines could use different ways to pass on the keywords info in the URL and its the tracking is not always 100% accurate to capture the keywords In the cases where default keywords i.e. Query parameter q=Search Keyword is replaced by h=Search Keyword, might not be captured by the Analytics tools. It totally depends how the keyword was passed in the query string by the search engine. May be someone else can give more ac...

Create paid search rule based on the condition you have specified in screenshot you should create Paid search detection rule. Then in Marketing channel rule use Paid search detection rule.