Let me answer your first question , difference between and satisfaction and happiness
The act of satisfying, or the state of being satisfied; gratification of desire; contentment in possession and enjoyment; repose of mind resulting from compliance with its desires or demands. "The mind having a power to suspend the execution and satisfaction of any of its desires.
Finding happiness is like finding yourself. You don't find happiness, you make happiness. You choose happiness. Self-actualization is a process of discovering who you are, who you want to be and paving the way to happiness by doing what brings YOU the most meaning and contentment to your life over the long run.
Second question : Both are essential to lead a peaceful life
Third question : How is peace linked to them ?
Ans :Theoritically the more you are satisfied , the more you feel happy , the more you are happy the more you are releaved from all the troubles, the more you are releaved the more you will be peaceful.
So it's all inter linked
Thanks for reading