Kinda - you could create a separate product for the deposit and add that to the cart, instead of the full price product.
For more control over what’s exactly added to the cart, a custom snippet can also be used:
Basic Custom Fields probably does the trick for you. The date type will validate the submitted value to be a date, and can be set to be required as well.
There’s also a PickupTime extension, but Basic Custom Fields is more flexible.
That sounds like a very specific report which is not available out of the box. There are a variety of reports, including product related, but I don’t think they match your exact business rules.
Might need to build a custom report: https://docs.modmore.com/en/Commerce/v1/Developer/Example_Modules/Add_Report.html