you backup before formatting your hard drive because when you format it gets rid of EVERYTHINg, so essentially you COULD backup after you format, but then you would have nothing to format, so backup before, then format, then put all the backed up data back
you copy all the original files to a another hard disk or flash drive before formatting the disk with the original files
Of course, copy all your programs and files you need from the old hard drive and put it on your new hard drive BEFORE formatting the old hard drive. Formatting your hard drive will mean losing everything and a slim chance of getting it all back.
If it's not already there after the hard drive replacement, then it should be on the backup you made, if you made a backup, if not, swap hard drives, run the backup wizard, reswap hard drives, restore from backup
I am guessing you mean "Do backups stay in the PC after Format?" The answer is No, if you store the backups of the files on the same hard drive you are formatting. Its not technically a backup then anyway. To make a proper backup, you need to copy your files to a USB key, burn them to a CD or DVD, or copy them to another computer or hard drive.
By formatting the hard drive.
When you reformat a hard drive you change it to whatever formatting you have selected and it will overwrite whatever format was used before.
To completely clear your external hard drive: On Windows: Connect the drive to your PC. Open File Explorer, find your drive under "This PC." Right-click on it and choose Format. Select a file system (NTFS or exFAT) and choose Quick Format (or leave unchecked for a full format). Click Start to erase everything. For a more thorough wipe, use software like CCleaner, Coolmuster Data Erasure, or DBAN to overwrite the data so it can’t be recovered. On Mac: Connect your drive to your Mac. Open Disk Utility (Applications > Utilities). Select the drive from the list and click Erase. Choose your file system (Mac OS Extended or exFAT). Click Erase to format it. For secure erasure, click Security Options in Disk Utility to overwrite data. Just make sure you're erasing the right drive, because it's permanent!
Yes.
Low-level formatting
Yes, formatting a computer hard drive will delete the operating system.
Yes.
Use Disk Utility to format or partition hard drives. You should back up the drive before formatting or partitioning.