Is it necessary to format a new hard drive?
Yes it is generally.
External drives would probably come formatted to FAT32 but internal drive unformatted.
So the purpose of formating the new drive is to set up NTFS?
It’s to set it up with a file system yes. Whether FAT32 or NTFS (in a windows environment) is the users choice.
When I bought my 2 Seagte external drives they were supplied formatted FAT32, so I immediately reformatted as NTFS.
Supplying unformatted is sensible as Windows is not the only O/S used and an NTFS formatted drive would need reformatting anyway for a Linux or Mac system.
You should format a drive, perferably in a cli-environment that way you’ll see if any sectors are damanged etc.
Yes, and I would do an NTFS format instead of FAT32. I never run FAT32.