Is it possible to highlight or mark the tasks that you have completed?
Please clarify what do you mean exactly with highlighting completed tasks? You can check a task off by clicking on the box on the left side of it. If it's a parent task - it will be removed from the list, if it's a sub-task it will stay grayed out until the parent task is completed or you hold down the SHIFT key while checking it off.
After that, you can click on the circular icon at the bottom of your task list within any project to see completed tasks.