Hi,
1 & 2) By default the plugin does not exclude items which does not have connection to the filtered taxonomy. In most cases this is expected behaviour, but it can be changed.
In you case I suggest this configuration: https://i.imgur.com/hOUaM7S.png
You can try playing around with these options a bit to get as close to the desired results as you need.
3. Checking your configuration I believe the match is very likely found within the content field. If the result is there it must match somewhere from the selected fields. Try turning off the search in content (or use a filter for it if needed) to disable content searches.
4. By default when hitting the magnifier and return button the plugin redirects to the default WordPress theme results page. You can turn that off here.