This Is Dictation.I understand your problem.
A foot I put together computers for many years and repaired store-bought computers for others. Hard drive problems are serious and are not easily corrected. The best you can expect for a drive that is been badly damaged is it you may be able to recover most of the drive and use it as a backup medium.
The operating system requires that the drive be very reliable. Most hard drive systems have a very high level of reliability, but when they fail they can feel very badly.
The most conservative approach would be to remove the drives are presently in your system and put in the new drive. Install Windows 10 on just a new drive and get it up and going and install whatever programs you normally need. When you get the point when you're satisfied that the new drive and the new install of Windows 10 is perfectly working, then you could try to recover some your data off of the other drives.
The most important data you want to recover is everything found in the my documents folder. That should include your photos, your videos, as well as any spreadsheets or documents that you been working on.
Recovering your e-mail can be more of a challenge if you do not have a system for doing that. Most e-mail clients have some privation for exporting your e-mail. Unfortunately, if the system is not working it's hard to export the e-mail.
However, when you reinstall your e-mail client it may be able to read your e-mail data from the old drive.
Another item you're interested in would be your books marks. And if you have a password manager, you want to retrieve your password data.
Of course, if you're in the habit of making regular backups to a cloud service or to an external drive then this should not be much of a problem for you.
Again, the most conservative approaches to do a clean install of Windows 10 on the new drive and work from there.
And yes, Windows 10 does have some recovery solutions, but these cannot be relied upon if the drive is in serious trouble.