Hi,
1. Depending on the filter types, I recommend checking the taxonomy term a and custom field filters documentation. Then you can set the search settings to a block position and to display automatically.
2. This documentation will help you with that.
3. The issue is caused by this file: https://uniscopio.com/wp-content/plugins/salient-core/includes/nectar-addons.css?ver=1.9.6
I believe is the nectar addons plugin or something similar. I am not sure why this file is enqueued on our plugin back-end, they may have forgot to add conditional checks where to load their assets.
Disabling the plugin temporarily will resolve the issue.
4. Your best option here is to use the result individual pirority settings. That will make sure to always prioritize the results you configure.