1) When I open a file through DOpus, no entry is added to the master MRU list (I.e. Start -> Documents). Is there a setting to enable this? You means Windows recent list? If so I don't know of a way for Opus to do that, however Opus does have its own internal recent list. Not for files, the recent list remembers the most recent folders you've been to. It also has a smart favorites feature you might find useful, both can be set up in preferences.
2) Is there any way to make DOpus retain the sort order when switching from one folder to another?You might give a read to this thread.