MacOS – Restoring Preferences after downgrade from El Capitan to Yosemite

I had the same problem as you few years ago.

You definitely have the sympthoms of bad sectors. If you can't backup with Time Machine I advise you to back your data from the finder by yourself and skipping the files that can't be read.

Edit : You won't be able to backup all your files. You can't retrieve the data stored on the dead sectors.

Honestly I would make a clone of your current drive onto an external HD. Then boot from it to make sure it works.

Once that is done I would boot from your Mavericks install key (unplug your backup drive!), reformat the drive and install Mavericks. Once that is done boot to the fresh install and do all of your updates so you have the latest version of 10.9.

I would recommend doing all of this from a username/account that is different from the one you normally use. Migration Assistant will re-create your old user account later.

Re-install your applications (I would do this as there may have been Yosemite-specific) updates that were applied to your apps that Mavericks might not like).

Then use Migration assistant, point it to your backup drive and have it migrate your documents and settings to the fresh install of Mavericks. I would avoid migrating the apps for the reason above.

Now, hang onto that backup drive and make another clone before you do any point (10.10 to 10.10.1) or major upgrade (10.9 to 10.10) to your OS, so you can revert more easily in the future. I always do it, yeah it slows down the upgrade, but speeds up fixing the upgrade if it breaks your software.