Our definitions are based on JSON schema and, as such, the default is to use strings for dates. The date controls in our forms engine let you customize the format string so that you can store ISO 8601 or other formats (perhaps simplified formats) as per your preference. The advantage here is simplicity with these controls and compatibility with JSON schema. The disadvantage is that MongoDB provides a lot of very powerful capabilities for range query and sorting that do not play as nicely with the simple string format.
If you wished to store some other format (such as an object where fields are broken out), you can implement a custom field type. For example, you could extend the out-of-the-box date control and have it work against an underlying object structure if you wished.
As far as I know, there aren't any date operations built into the core Dust tags. However, customers do frequently implement their own tags. See the section on Customize Dust here:
https://www.cloudcms.com/documentation/appserver/appserver/overview/module.html
Implementing your own custom tags require that you run your own instance of the application server. You can do this either by building a custom Node app, running standalone or using our Docker image. These are all described here:
https://www.cloudcms.com/documentation/appserver/appserver/overview/overview.html