Hi!
Position
The position issue is due to the fact that the search bar is placed within another element, which gets hidden whenever the scrolling begins, but the results list tries to maintain the searches last position. There are two possible solution I would recommend:
1. Change the results layout from ‘hovering’ to block: https://i.imgur.com/dfwh7v7.png
2. ..or try the following option: https://i.imgur.com/DRP22nK.png
I personally recommend trying the 2. first, it may actually work.
In case the plugin finds more results it can display a ‘show more’ button, you can enable that here: https://i.imgur.com/otPLW5Q.png
Permalinks
I have visited both links, but both of them work and lead to the same page. The plugin uses the internal [php]get_permalink(..)[/php] WordPress function, which returns the permalinks as configured on the back-end.
Do you use any custom SEO or any other plugin to change the permalink structure of certain posts by any chance?