Hello @psartorio,
Thank you for your query.
Regarding your questions
1. The search field does work with Ajax now partially, however, after typing 3 letters it will not show the result for now. we may add this in a future release.
2. The search field looks for package title and also on category, tag and date based on the selected option. You should be able to check the demos from the below page.
WPDM Directory Add-on
3. Yes, it’s possible by customizing the page template. Please check the below docs for more info.
Template Files
And available template tags can be found below.
Template Tags
I hope that helps and answers your query.
Regards