Error in database export
Do I need to increase undo_size? …


Yes, that is exactly what you need to do. The export needs a consistent MVCC snapshot from the start of the operation. UNDO_RETENTION is ignored if your UNDO tablespace is fixed size or can't be extended:


  UNDO_RETENTION specifies (in seconds) the low threshold value of undo retention. For AUTOEXTEND undo tablespaces, the system retains undo for at least the time specified in this parameter, and automatically tunes the undo retention period to satisfy the undo requirements of the queries. For fixed- size undo tablespaces, the system automatically tunes for the maximum possible undo retention period, based on undo tablespace size and usage history, and ignores UNDO_RETENTION unless retention guarantee is enabled.


  … How it [undo size] should be calculated based on my database configuration?


It needs to be calculated based on how quickly you are generating UNDO (with DML), and how long the export takes — you'll need to find a size that works for you or try and do the export when less UNDO is being generated, or speed up the export. If you have the space available, increasing the size of your UNDO is the easy solution.