export and expdp are NOT BACKUP tools, they are data copy tools, they are NOT BACKUPS.
full backup:
http://docs.oracle.com/docs/cd/B10501_01/server.920/a96519/glossary.htm#432659 as stated there, a full backup does not refer to "how much" but rather "how" a single file is backed up.
Now, in general, many people (self included) think of a full backup as:
a) control file backup
b) plus datafile backup
c) plus any archives needed to restore and recover b with
d) parameter file backup
you never never never backup online redo logs. never.
b) a cold backup by definition means the database is cold, stopped, not hot, cold. You ALWAYS stop the database before a cold backup by definition.
c) because that is what the word 'hot' means - that the database is in fact 'hot', up, running, doing stuff, not cold.
d) hot, only - if you ask me.
archives: you need to keep all archives that were generated during/after all of your backups. You can release these archives (remove them from tape, disk, whatever) AFTER you remove the backups they are needed to be applied to (because you keep AT LEAST your least two or three backups).
You backup these archives ASAP - and get them mirrored on another set of disks elsewhere or on tape elsewhere. They are crucial for recovery. Just as you do not keep your backup on the production machine (because if the production machine burns up in a fire....) you do not want to keep your archives there long either.