Connecting cables when end point rotates 360
You have two possibilities:

A slip ring (or multiples for each cable). Advantages are that you can easily run mostly the same signals signals as over your cables. Disadvantage is that it has contact wear and isn't suited for high rotation speeds due to that.
Example: 

Rotary transformers (again one for each cable) like in VCR heads. You can only use AC signals here, it is more complicated to build, but you can do it in higher speeds.
Example: