Adding a new column with a unique name on the board automatically creates a corresponding status and Creating a new status in the project workflow will automatically add a new column to the board are correct.

Team managed projects keep board columns and workflow statuses synchronized so adding a column on the board will create the matching status automatically and creating a status in the workflow will add a corresponding column. This behavior lets project admins manage the board and workflow from either view and the platform handles the mapping for you.

After you add a status in the workflow you must manually place it on the board or it will not be visible is incorrect because a new status in a team managed project is reflected on the board automatically and you do not need to place it manually.

Only a Jira global administrator can add new statuses for a team-managed project is incorrect because team managed project administrators can add and manage statuses for their project and a global administrator is not required for those project scoped statuses.

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