How can I connect CCBS parts to plain LEGO system? Can anyone explain how the front shoulder was built in this MOC? 



Are there bricks that allow easy connections between CCBS and plain System?
There are several parts that make this possible. Many of the CCBS-style ball socket parts include Technic axle connections that can ultimately be attached to system bricks (e.g. 93571 and 50923). There are several examples of this in the Exosuit (instructions):



There are also several Technic ball socket parts that include System studs such as 57910:



Here's a list of Technic bricks with ball sockets that might be helpful.

There are also other connections that are shared between CCBS parts and system, such as bar connections, you just have to get creative. Feel free to ask additional questions if you are having trouble integrating particular parts.