Hi,
#2 – While this falls under customization requests, I might be able to suggest a possible solution. This will work only if the auto populate is enabled to a search phrase (does not matter what phrase, leave it empty).
The first section of this code will overwrite the auto populate phrase, if the wpv-category query variable is set. Another possible solution would be to auto-check the category based on this variable, but it is much more complicated – as the category ID would have to be resolved first, then a custom script must auto-check the desired value. I am not sure if that is even possible to be honest.
The second part will make sure to clear that phrase, whenever anything is clicked on the settings box.