Thank you very much for the rating, I greatly appreciate it!
For the suggestions: You can change that on the Autocomplete & Suggestions menu. I suggest using the “Post titles”, “product tag” and the “product_cat” as sources: http://i.imgur.com/lhkiFUG.png
This way, the product titles and tags will be used in the autocomplete suggestions. It’s not as good as google suggestions (to save server performance), but it’s better than nothing 🙂
Unfortunately it is not yet possible to use the index table as source for search keywords (but it will be implemented soon).