Hi,
Thank you very much for your kind words!
1. Do you mean like an order-by feature? Unfortunately that is not possible yet.
2. There is no option for that. There are however API hooks, which can be used to access the results programmatically. The asp_results hook might be interesting for you, as it contains the results for the given search phrase. In case you will have this custom coded, this might help a bit.
3. You can set the default states of the checkboxes for each taxonomy here: https://i.imgur.com/3yBk0yG.png
