I think you can try to:
Enable Path for your org. From Setup, enter Path Settings in the Quick Find box.
Click Enable. To let users decide whether the path remembers its previous state, select Remember User's Path Preferences. If not selected, the path’s details are hidden when the page that the path is on loads. To Enable Path user should have Modify All ...
No. Related lists cannot be filtered this way. You could create a custom component or Visualforce page, or build a solution involving record types, multiple page layouts, multiple lookup fields, and a few triggers or processes.