Hi!
Thank you very much for your kind words, I really appreaciate them!
1. It is possible, this documentation will explain everything you need.
2. You can create filters based on taxonomies or custom fields. In case of products, you are probably looking for taxonomy term filters. It also worth reading how the settings layout is handled.
3. Sort of. You can have both autocomplete and keyword suggestions to use contents from your site. Google is much much faster, as it runs on a external service.
4. Yes. You can prioritize some results individually (whenever they match), as well as create groups for more complex uses.