1. Logs which are (currently) unarchived are referred to as redo log files. When these files get filled up, they are copied to a archive destination and are thus called archived (redo) log files.
2. Correction: a ts is not offline during a hot backup, it's in backup mode. Changes are logged in the redo log files.
Archived Logs are copies of the Redo logs.
When running in ArchiveLog mode the Archiver process archives the redo logs as they are filled and the new log grouup becomes active.
You will need these archives if the database crashes and you need to restore from the old backup. In that case you will need all the logs archived after the last backup was taken.
When the tablespace is in backup mode the changes are logged in the redo logs. It may be a good practice to Archive your active logs after the tablespaces are brought out of the backup mode. This way you make sure that the all the redo generated during the backup process is archived as well.