Hi Miguel!
1. It’s only doable, by using the same search instance on the results page as well. Using different search instances will yield different results, as it is not possible to pass them from one to another, and the selected options will be reset as well. While using the same search the settings are memorized as well.
2. The auto populate will respec the selected filters. I believe the closest possible solution is to set the filters as you need them initially, then configure the auto populate for an empty search phrase: https://i.imgur.com/TerfYGT.png
3. If you mean in hovering mode (default), the results display above the settings, then you can change their z-indexes under the theme options panel here: https://i.imgur.com/XHYAYN9.png
The higher z-index is displayed on top of the other.
