Can i livestream like Minecraft in Full HD in 60 fps with a GTX 960 and a i5 6600k?

Yes, you can. But, make sure you have high speed connection

The critical combination of CPU and capture card and your INTERNET OUTBOUND speed have much more to do with the livestreaming. Very few people even try 60fps due to the limitations of the users who view your stream! Do you really think they can "see" the difference between 30 and 60? Most can't. However, if you want to try that you need the i7 to prevent processing delay in your stream.