1. I don't know the answer to this, but if the computer hard drive goes, are files actually deleted? Because if they are, then when the external drive does its automatic backup (after which its contents will exactly reflect the contents of the computer's HD), the files would be deleted from the external drive as well. That is, the external drive is a "backup", not an archive. The files on it are only as permanent as the presence of the same files on the computer's HD.
The answer is, it depends. It depends on how the work hard drive fails and how the backup software is configured.
As for the hard drive going bad, generally speaking, the whole hard drive doesn't go kerfluey. A sector goes bad here, a sector goes bad there. Things start acting strangely. If a sector goes bad where, say, the boot image of the operating system lives, the drive no longer boots. Yet you can still mount that hard drive on another system and copy the uncorrupted files from it, skipping the bad sectors.
As for whether deleted files are still on the backup disk, most backup software has a switch that controls this. Rsync calls it "delete on destination." The option tells the software whether to delete old files on the backup disk that are no longer to be found on the work disk. Personally, I do have it delete old files, so that my backup is a mirror of the work disk. However, others take the equally valid approach that they do not want anything deleted on the backup. They do this not because of any disk failure worries, but because of human error -- if you delete something and later decide that you shouldn't have deleted it.
2. A catastrophic loss of the contents of the computer HD and the external HD can occur with theft, fire or lightning strike.
That is true. For offices, I like to advise two backup hard drives. You back up Hard Drive A today and take it home. Next day, you take Hard Drive B to the office and back it up and take it home. That way, there are two backups, a maximum of two days old, and two locations. If something catastrophic happens to cause you to lose your home hard drive and your office hard drive, chances are that data loss is the least of your worries.
For both reasons, it's a good idea to archive, on DVDs or CDs, your photos and files that you couldn't stand to lose, and store them in a safe place, like a safe deposit box.
Some "experts" suggest that CD-Rs and DVD-Rs only last about ten years, though.