@FP 

With regard to item 1, connect a Workflow variable from Nintex Workflow to a list column, you need to use a Set field value or Update item action to set the column's value = to the variable.  If the variable value will change through the phases of the workflow, you will need to include a new Set field value or Update item action to reset the field value.

With regard to item 2, How to connect a Workflow variable from Nintex Workflow to a list column in Nintex Form, I'm not sure why you would want to do this.  A workflow variable is only valid while the workflow is running.  Once the workflow completes, the variable no longer has any use.  If you update the column value in the workflow, the form will display that value, so long as the field is connected to the column you updated.