yes, this is possible. There is a field type called “Last modified time”, for which you can specify to which field it shall apply. That shows you how long a card has the same status (Kanban boards just being a different visualisation for the single select / dropdown field).
For the second part: You could create a color based on conditions. The condition would again be based on the “Last modified time” field. As an example: Apply color green IF Last modified time is less than 3 days.
Hope that helps!