Restoring Oracle Database using Rman
Both errors indicate that you need more archive log to complete media recovery and bring your data files to a consistent state. 

If the datafiles are newer than the redo data you have available, the the alternative is to grab an older backup of the datafiles and work from there with the redo data you do have from the latest backup run. A common strategy is to continuously send archive logs to a backup destination between backups, and in that way minimizing the loss of data leading up to the next scheduled backup.

If you would rather aim to get an independently consistent backupset, you need to capture all the datafiles as well as all of the redo generated while backup was running. I would suggest something like this sequence of backup operations:

run{ 
backup database ;
sql 'alter system switch logfile';
sql 'alter system archive log current';
backup archivelog all ; 
}


Note how you would first complete the database backup, then force a switch to the next log group before triggering an archive process and finally start backing up the archived logs. Those logs now have a much better chance of containing the redo data you need to run media recovery on files restored from this backup set.

UPDATE: 

In your current situation, if this really is all the data you have to work with, I think you should still be able to bypass the ORA-1547 by pretending to do a manual incomplete media recovery and then open with resetlogs.

STARTUP FORCE MOUNT
RECOVER DATABASE UNTIL CANCEL;
CANCEL;
ALTER DATABASE OPEN RESETLOGS;