I have a iPhone 5s with the iOS 7.0.4. I have many apps in the phone which are free ofcourse and some paid apps. Can i manually back up the iPhone before jailbreak and restore the back up again after the jailbreak, to get all my apps that were before on my iPhone?

You don't Restore after a jailbreak because you will lose the jailbreak. When you jailbreak there are two sets of apps. The original apps that came with IOS 7.0.4, and any jailbreak apps that you will download from Cydia after you have jailbroken your iphone 5s. So you need to follow the Iclarified Wizard for jailbreaking. 1. Backup your iphone through iTunes 11.1.3.8. 2. Download the IPSW for your iphone and store in PWNAGE folder. 3.Download Evasi0n 1.0.5 from Evad3rs. 4.Run Evasi0n after installing it. Now if you want to Backup any Cydia Apps that you download, you need to purchase PKGBACKUP from Cydia. In the future, you will need to do periodic backups from iTunes and Pkgbackup to cover all your apps.