How to show new nodes in a Group node view for users who are not a Group member?
... After creation the node is not listed in the group nodes ... While checking it, the user is not a member of the group. If I add the user as a member it works fine.


I'm reading the above like "For users who are not a member of the group, I want the nodes to be listed in the group nodes also". To implement this:


you need to correctly configure the permissions for what in the Group module is called "Outsider".
you should NOT have to "add members dynamically while creating node in the group", as in your question (that's not how the Group module is supposed to work or be used).


And to configure the permissions for Outsider, you can use either of those techniques (using Group-Type-x to indicate the type of group):


Grant permissions to group role at /admin/group/types/manage/Group-Type-x/permissions, so that a user who is not member of a group, receives the Outsider permissions for that group.
If you need to distinguish between outsiders based on what roles they have in the global scope, then (and only then) you should use the "Advanced outsider permissions" page, located at /admin/group/types/manage/Group-Type-x/permissions/outsider. There you'll find all roles as defined in /admin/people/permissions (= the global scope).


With the above in mind, and looking at your question details, it seems to me that there are 2 possible solutions (depending on how you want it to work):


If all outsiders should have similar access Then Tune the Group permissions at /admin/group/types/manage/Group-Type-x/permissions.
If outsiders of selected global roles should have specific access Then  Tune the Group permissions at /admin/group/types/manage/Group-Type-x/permissions/outsider. Note that the image shown in your question (about "Advanced outsider permissions") does not show anything that you already gave some permissions to role "Manager" (there is not even 1 checkmark below role "Manager").


BTW, about your "If I add the user as a member it works fine.": that seems to confirm that you correctly configured your permissions for members of the group. But by "adding a user as a member", such user is no longer considered an "Outsider". So you really need to fix your permissions for "Outsider".

PS: If for Anonymous users you want similar access permissions as for  "Outsider", then you also need to configure those permissions via  /admin/group/types/manage/Group-Type-x/permissions.