You want to ignore your operators status completely.
If you want to show invitations without any operator being online you can check also checkbox in
Chat configuration
Online tracking
Should invitation logic be executed if there is no online operators
To archive 1 point. You have to set department online hours. It can be done by editing department
To archive 2 point. You have to go to chat configration, Misc and at the bottom you will find "Ignore users online statuses and use departments online hours"