Ok. Just to open the database (without regarding data loss) from a cold backup, all you have to do (provided your cold backup contains all datafiles, control files, and log files), is to restore all the files from your cold backup, then you should be able to "startup" from svrmgrl. No need to worry about database recovery.

Test that to see if it works. If it doesn't, do you have all of your datafiles, control files, and log files in the backup? Was it taken while the database was closed?

Once that opens, shut it down, and restore the cold backup again. Now you can try to get back data that was commited after the cold backup was taken.

Restore all the files from the cold backup
svrmgrl> startup mount
svrmgrl> alter database recover until cancel using backup controlfile;
-- here it should start prompting for archived logs
svrmgrl> alter database recover continue default;
-- repeat that until there are no more suggestions, or when you apply it it says "no such file or directory"
svrmgrl> alter database recover cancel;
svrmgrl> alter database open resetlogs;

The second method assumes you have the archived logs from the database. However it looks like you might not have all of the archived logs available, or they are corrupted.

00310, 00000, "archived log contains sequence %s; sequence %s required"
// *Cause: The archived log is out of sequence, probably because it
// is corrupted or the wrong redo log filename was specified