1. In “NO ARCHIVELOG” mode, you can take only closed backup, which is consistent and whole DB backup and upon restore does not require recovery, hence no need to have redo log backups.
2. In “ARCHIVELOG” mode, ARCH process/s are archiving the redo logs.
3. By multiplexing the redo log file(multiple log member in a redo group) on separate disk/spindle will protect from single point of failure(SPOF)
4. Main reason not to backup redo logs is to avoid the scenario during restore, where existing online logs are overwritten by the backed up redo logs, which will create issue during complete recovery of your database.