Hi @JennLong ...
One thing you can do (but may not fully meet your needs) is to lock your modules until a date/time that you specify. When you are on your "Modules" index page, click on the three vertical dots icon (also called a "kebab") to the right of the module name. Then, select "Edit". You will find a "Lock Until" checkbox. You can then select a date and time for when you want to open up that module for your students. You could keep the items published within that module.
Again, this might not fully meet your needs because there isn't a date/time field where you can specify when to unpublish or not make the module material available again.
For your assignments and quizzes, why not use the "Available from" and "Until" date/time fields? You could set those up so that those items are only available between the dates that you set in the properties for those kinds of assignments/quizzes.
Do you think any of this might work for your needs? I know that you said items show up on the "To Do" list, so you might want to test that out as you play around with these settings.
I hope this helps in some way. Sing out if you have any questions. Thanks!