Is there a way I can give Read & Write permissions to myself for System files on Mac OSX 10.11.2
Solution 1:
El Capitan has a new feature called System Integrity Protection, which restricts what you can do even with admin or root access (see this apple.se question. Among other things, it prevents you from modifying /System.
It is possible to turn it off (again, see that other question), but it's generally a bad idea. You shouldn't be modifying /System without really good reason. Local customizations should generally be made in /Library instead (that's more or less what it's there for).