A: Yes. A saved list stores the values you entered in the search fields. Each time you open it, the search runs again on your current data.
When you change the search fields, a Save list button appears next to the list name at the top of the page. If the list is one you can edit, the button reads Update list, and its menu has Save as new list. You name and share the list the same way as any other list: see How to save and share a list.
The list AM Sales is a saved list for the search where account manager is in the role Sales.