I had heard that Trello could take an end due date and help you schedule what tasks should be done by a certain time, but can't seem to find anything showing that it actually can. Can this be done?
You can set the due date of a card by clicking the "Due Date..." button on the back of the card. You'll get a notification 24 hours before it's due if you are subscribed. Trello doesn't have have a way to suggest or scheduling due dates though.
In addition to assigning a Due Date, you can add the Calendar Power-Up to enable visual scheduling. Just go to the Menu on the right and select Power-Ups to enable this feature. As you can see in this example, it provides a calendar view of your cards and makes it easy to adjust due dates and schedules.