Yes, you can assign this delivery date feature to any shipping method, thus you can allow customers to choose delivery date and time if they select only particular shipping method/methods. Read on to see how to make the configurations.

Yes, if needed, you can change a delivery date and/or time via the Magento admin panel. To see how to make it correctly, read the full answer. 

Yes, there are three main date formats configuration you can choose from. Follow a complete answer to learn the settings.

Yes, it's possible. In case you wan to limit delivery time for same day orders, you need to enable the 'Disable Same Day Delivery After' option and set a time period you need. 

Yes, this data can be added to the grid. You can also sort orders by delivery date or time. Read on to see the settings.

Use one of the examples described in a complete answer to get such shipment info as a delivery data by API.

A Delivery Date can be shown in pdf invoice via settings made in the 'Include Into' section. Go on reading to learn how to make it correctly.