Thanks for bringing this up. Haven't reviewed the Google Search Connector for some time.
Hopefully the bug you describe with restarting will be fixed in the next release which will be available shortly.
Capturing the ads is very tricky, and Google has introduced additional variants of presenting ads which means new html formats. When I wrote the connector, it was meant to capture the "text-based" ads. Will look into ways of scraping the "image-based" ads. Here is an example of three different types: