Hi Bjarni,
You won't be able to password protect a web map hosted on ArcGIS Online. However, you could share the web map with a specific group(s). Only users that are members of the group will be able to view the web map.
I am not exactly sure what you mean but simply yes.
If you share the map with certain people and then send the link. Anyone who tries to open must enter credentials for one person in the group.