Is there any way to explicitly delete a file?
Does the reader maintain a cache of documents
And delete the least recently used?
If so, how large?
You can delete a file by going to the Documents view (tap on "Documents" if in Recent Files). Then, you can swipe on the file name to the left or right and a delete button will appear.
The Reader keeps all documents that you've read in the Documents tab with no limit. The recent files list is 30 files long and is just a reference to files in the Documents tab (as opposed to a copy).