1. I am not able to see the reason why the start date shows 01/25/16 but it could be based on the start date of the Project (not shown here). Could this be the reason? You do not have any dependencies (Predecessors) which would set the Start Date to the earliest possible date according to the Project, not just the Milestones/Tasks.
2. This is a strange one. I have no idea why the start date is incorrect. I do see that the Start Date and Duration have been manually set (blue triangle in top right of cell) but the Due date should have updated accordingly. There may have been a problem with the recalculation. Please try to change the Due date manually and then restore it to see if the date adjusts to the correct dates. If it does not, please open a support ticket. Provide URL link to this Task, this screen capture and Temporary access link so that we can review what the problem is.