RMAN archives deletion

Am a bit confused about what exactly is your question(s). Let me see if I can answer (at least) some part:

Never been able to fully grasp the notion of delete input/delete input all when backup up Archivelog with rman.

I believe you are talking about DELETE INPUT part of the syntax of BACKUP command. This part tells oracle to delete the archived logs that exist at the time BACKUP command is run (as well as those generated during the execution of BACKUP command) ONLY AFTER BACKUP has successfully backed up the archived logs. Without this part, the archived logs are not deleted.

Deleting input, or deleting input all, seems counterintuitive to me when the deletion policy is set to 7 times to match an overall backup policy of 7 days.

A deletion policy is used by Oracle to manage the space in flash recovery area. Oracle can delete archived logs in flash recovery area when the flash recovery area is full and there exist archived logs that satisfy deletion policy criteria i.e. if deletion policy criteria is set to 2 days and the flash recovery area gets full, say, on Thursday then oracle will automatically delete archived logs older than 2 days (i.e. before Wednesday) to free up the space.

And what should the Archivelog deletion policy be if the goal is to have one week’s worth of backups available at all times?

That depends upon a) How much data loss is the business/company is prepared to tolerate? & b) What is the SLA (Service Level Agreement) time for recovery of database & c) your backup strategy (hot/cold, full/incremental, image copy/backupset etc.)

Hope this helps.

SET NEWNAME works for RESTORE and SWITCH, but not for RECOVER. Datafiles had been renamed and switched before the recovery started.

There is a flaw in your process though, and the above issue is its side effect:

Restore the control file from the 3/9 backup.

Why? You do a nearly complete recovery to get as close as possible to the current state, not the state on 3/9. Restore the controlfile from the latest backup taken on 3/14.

Since the restored control files aren't aware of the backup pieces for 3/10 - 3/14, I run this for each

This step is unnecessary if you use the latest controlfile.