Let’s try to address your questions. Though, I’m afraid some of these will not be possible to be achieved due to the way the system works like 🙁
1. This can be easily modified by going to the Customiser -> Header section, then clicking on the search element and modifying the criteria to only show products — https://ibb.co/sRS97vk. This should bring back the whole WooCommerce loop when you search for stuff.
2. Unfortunately, this isn’t possible as the live results are meant to only preview what’s on the website at a glance.
3. Hmm, not so sure about this one. What kind of modifications are you trying to accomplish? The Type 2 cards are meant to have a unified look here and what you’re seeing is the expected behaviour.
4. This is sadly not possible (at least for now) due to the way WooCommerce works like. I will try to note this down in our feature requests list for future consideration.
5. This is completely up to the plugin’s developers and what are they offering. If they offer this as a shortcode, that would be your best bet. I would try using the HTML area instead of the widget one. You should have more control with that.
Hope these answers help! 🙂