it sounds like you should be using events instead of tasks...
1. tasks don't show up at the start time, they show up at the start date
so you know what you have to do that day. they remain visible until they are marked as complete. they do not automatically turn become marked as complete after the due time. instead, they change to overdue. depending on the skin, overdue items might look different, but it's an option that the skinner has to add. tasks disappear when deleted, or if you set them to hide when complete, they disappear when marked as completed.
2. returning at their start time? that's not the nature of this program, nor is it the nature of "to do" items. they return either immediately, or on the day they start, depending on how you set things up (see #3)
3. right-click on a todo item like i suggested in my previous post, then choose "hide upcoming tasks". that way, only today's items will show.
that is how rainlendar works. if it's not how you want it to work, then perhaps you need to write your own program