Diagnostics already includes syslog since the last reboot, so no need to post separate syslog.
You should never format a disk with data on it that you want to keep. You should have asked for advice and we probably could have helped you recover the data.
Disk2 SMART is OK but it seems to have connection problems. Double check all disk connections, power and SATA, both ends, including power splitters.
Are you sure it is a disk making the sounds?
Looks like you have some problems with mover and duplicates, which is keeping you from getting your appdata, etc. moved to cache. We can deal with that later.