1. Sit tight for now. No more diagnostics of any kind. yes.
2. When USB gets here, do the USB backup. yes.
3. Run the chkdsk /f C: before I start the transfer process to the new hard drive?No.
1. Check the USB backup to make sure it is accessible and your files are there.
2. With the the PSU disconnect, remove the SATA signal and power cables from the old HDD.
3. Install the new Drive, > Clean install of the system, set up as you want.
4. Run and test the computer to make sure you have no more issues.
5. connect the old drive, > transfer your Data.
I would not bother testing the old drive, providing you are sure there is nothing on it you need.
Wipe the drive, > perform a extended format, then test to see its condition.
Possible keep it for backups but if in doubt, dump it.