Jailbreak iOS 6.1 for iPhone 4S requires to disable the Passcode lock of your iPhone, because it will interefe with the jailbreak and cause errors. Read More
Redsn0w on Linux version is not available for you to download, but there are many ways that allow you to run windows software on Linux machines. Read More.
Tweetbot is a mobile application that allows you to use Twitter to your iDevice, and there are special versions for your iPhone, iPad and iPod Touch.
Jailbreak iPhone 4 GSM on 6.1.3 iOS version is possible with the latest Redsn0w version. Redsn0w 0.9.15b3 can perform a tethered jailbreak to iPhone 4 GSM.
If you are having problems with applications that you download from AppStore or Cydia, there is a general tutorial to do a basic troubleshooting to them.