When is the best time to use RMAN vs when to use Data Pump? And also... if I backup a database with RMAN, is it not possible to use impdp to restore small parts of that database?
The rman utility is for making a physical backup of the database that can be used to restore the database back to a consistent image for the entire database generally at the point of failure when combined with the archived redo log backups.  Datapump is for making logical point in time copies of data.  Forward recovery of the data to a point in time more current than the time of the export is not provided.  In an export row data may be at different points in time for different tables resulting in some minor data inconsistencies upon import completion.  Export may be good enough to use as a backup for test databases.  Both rman backups and export should probably be ran on production databases.