Can I Jailbreak my iPhone 4S 6.1.3?

If yes how? Risks & consequences? What can you do if you jailbreak it?

You can, but its a tethered jailbreak. There are alot of things that you can do to your iphone if you jailbreak but the main one for me was the themes.

Tethered means that everytime you boot up your iphone you have to connect your iphone to your computer and run a program to make your phone go to the lockscreen.

Nope, you can't jailbreak that device with that firmware.

There's no Jailbreak for that firmware unless you are on a IPhone 3GS with an old bootrom. The only jailbreak tool that is trusted is evasion for ios 6.1.2. All the other ones like silver wind are fakes. You can try and break your iphone if you want though.