DVD's I'm not sure but I copy my CD's to my hard drive using Windows Media Player or any other software that converts a song from CD format to MP3 or WMA formats. A MP3 or WMA file is about a tenth the size of the original. I have over 4 thousand songs on my hard drive and it only takes up about 15 GB of space. I don't think you can back up DVD's without special pirating software.
You will find 'dvd ripper' programs galore on the internet, many of them for free. But protected DVDs should not be copied as they are subject to copyright law.
Put into the CD and/or DVD ROM drive, open it (control-click or command-click to open so you see the files), then drag the files on the CD onto your hard drive icon.
Find a DVD Ripper to backup onto hard drive, for example, Magic DVD Ripper, which rips from the DVD disc and convert to other video formats for 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.
External hard drives do nothing on their own. Their purpose is for you to put data onto them. You could very well copy DVDs and put them on the hard drive, but they aren't going to do that by themselves.
You should perform regular backups of a hard drive at least weekly.
Daily backups are ideal.
Hard copy is like a audio CDs and DVDs
Same thing as in Windows. You need a DVD copy software to help you, I suggest you use Longo Mac DVD Copy from http://www.longodvd.com , it can automatically decrypter copy protections of DVDs and copy DVDs to hard drive or burn DVDs to blank discs easily.
If it's DVDs you want to back up to your hard drive, use DVD Shrink 3.2 or DVD Decrypter (Freeware, can be found with a search engine).
weekly
Yes.
external hard drives
No. No it won't.
Call data recover specialists like drive savers they will safely take backups and send you the data.Try to use Nice to Recover Data for Mac software,it can recover lost data with high quality.