I have created a list of items. The last column in my list is an "edit" this entry field (1)(2)(3). All permissions are set to public (1) and the menu item which runs the list has a permission of "Registered". On the front end a user with Super user permissions can see the list (4) and click on the Edit icon to edit the entry. A user with Registered rights, can see the menu item, can click on it and return the list (3). The edit column icon is not visible so such users are not able to edit the entries. Tried to attach four images to show (1), (2), (3) and (4) but "Medias" said illegal entry for *.jpg.
For edit button to render you probably also need to give them edit permission (what you are talking about is viewlevels that define only view permission)
Not sure what you mean, yu can set different edit permissisons for different groups on different content types, e.g. you can set users that belong to group A to be able to edit content type X and users of group B to be able to edit content type Y, but not vice versa.