If you can boot from an external drive, then you know the Mac hardware (other than the internal hard drive) is ok.
I would:
1. Get whatever I can from the internal, save it somewhere else
2. ERASE the internal using Disk Utility
3. Run DU's "repair disk" function on the just-erased drive
4. Do you get "a good report"?
5. If so, REPEAT "repair disk" 5 times -- do you get a good report each time?
6. If so, re-install a copy of the OS and try again.
S.M.A.R.T errors are a 100% indicator that an HHD is bad.
Only do the above if you want to waste a lot of time. The drive is what, 11 years old? Replace the drive. It is toast. Even if you get it showing ok in Disk Utility, the only advantage is that you'll be able to get all your data off. If you have a recent Time Machine backup, don't bother.
As for running repair Disk in Disk Utility, it repairs one problem at a time. Look to see if the error is identical—usually, it's a little different. If so run it again. Get the same error 3x in a row, give it up.
Let's say you get everything up and running. Prepare to do it again within 2 weeks—that's the longest I've seen. 10 hours or less is more likely.
DiskWarrior cannot help you do anything except waste $100. All it does is back up and rewrite the directory. It cannot fix anything caused by a disk error. It's only useful as a diagnostic tool — it sometimes finds bad drives before Disk Utility does.
I put an SSD in my daughter's 2008 iMac a number of years ago. Hers dual-boots into El Cap and 10.6.8 for an app she likes that was never updated further.
All you need are a few tools, the drive and one of these brackets. Replace the BR2032 battery while you're at it. These are very easy to do.
