I am building a VSTS dashboard widget where I would like to iterate over all Features in a particular Epic, and then for each Feature gather data about all the WorkItems to create a status report.
I know I can use getWorkItem() and getWorkItems(), but that is if I already know the WorkItem IDs. I want to loop through all the features and then all the WorkItems and see if they are completed, without knowing their particular ids.
The VSTS work item tracking system is very extensible, therefore there aren't any "fixed" methods that will return you specific work item types. Even though features in VSTS rely on one or more levels of work items being present, their name, the fields and other aspects of these work items are highly configurable.
To query the available work item levels (called Categories in VSTS), you can use the Categories/List API. This will allow you to find hierarchy as it's configured in VSTS and which work item types are available at each level.
You can use the ProcessConfiguration/Get API to list the relationship between the different backlog levels. Which is a parent of which and what type of backlog it represents. Is it a Task (lowest level), Requirement (Story, PBI level, planning level), or a Portfolio (Epic, Feature etc) level backlog.
With this information, you can either use the Backlig/GetBacklogWorkItems API to fetch all the work items on a specific backlog or you can construct a WIQL (Work Item Query Language) query to retrieve all work items that match that specific query. You can either export the WIQL from Visual Studio or use an extension.
Depending on what you need with each work item you can either query directly for the required fields, or just query the work item ID's and fetch the work item details individually using the workitem/getWorkItems(id) API.
There is pretty extensive documentation available on each of these API's and on the required VSTS services you can use from your extension. going deep to explain each of the services goes too far for this answer. I suggest you start experimenting from here and ask new questions as they arise. You now have far more information to work with and it will be easier to ask targetted questions from there.