Hi,
Thank you very much for the details, it helps a lot!
I tried to log-in to the back-end, but the username seems to be incorrect. Nevertheless, I think we might be able to resolve both issues without the access.
1. You are likely using the auto populate feature to show the latest results. Instead, please try the following configuration: https://i.imgur.com/qygzF25.png
It will trigger as if a checkbox was initially clicked, with an empty search phrase.
2. Try using the {_price_html} pseudo variable instead of the {_price} in the advanced content field. It requests the price HTML output from WooCommerce, and hopefully it should contain the same formatting as the shop prices.