How to get SharePoint group through Nintex workflow and add users to the group

Hi
Not sure what is your exact requirement, easy way is to create a list with Title and SP Group Name (single line text) columns. Fill the Title column with some identifier, and fill the SP Group name in "SP Group Name" column. Use Query List action to query this list filter by TItle column and get the "SP Group Name" column.
Otherwise, build a Dictionary variable with key/value pair and read the group name based on key value.
Having list is easy to maintain, with dictionary variable, you have to update the workflow for any changes.
Title SP Group Name
Visitors Visitors Group
Members Members Group
Approvers Approvers Group
Owners Owners Group Name

If you are using Nintex for SharePoint on-premise, there is no action to add a user to SharePoint group, "Add user to a AD group" allows you to add to AD, not to SharePoint group.

But you can try using web service action (works for 2013, 2016 and 2019), here is the link

If you are using Nitex for SharePoint Online, you can use action, "Office 365 Add User to Group" action.