There is clear evidence that decisions are made before they are expressed consciously.
I don't know that the evidence is conclusive, but let's stipulate to it being so. That sounds like what I call the illusion of free will - unconscious neural mechanisms generating will through some combination of determinate and perhaps indeterminate quantum-level processes which is received by conscious agent - the self or Freud's ego - which mistakenly understands itself as the original source, hence the illusion of free will.
That does not however in any way indicate that the initiation of the decision was not of free will.
I'd say it does. I say that if this process could be manipulated externally and the desires generated changed artificially, the self wouldn't know and would continue to think it was the author of those desires, because he is uninvolved in their generation, which is all an unseen black box to him generating output according to unseen algorithms.
Does a person decide when a joke is funny, or does some unseen neural mechanism process the joke and tell him what to think about it according to rules he cannot elaborate. None of us can say what the rules are for themselves for finding something funny. It's another black box that processes the joke according to unseen algorithms and delivers a conclusion: not funny versus worth a smile versus very funny. This seems similar. Just as the brain informs the mind of what is funny, it seems to also inform the mind of what it wants.
There is no evidence to show that free will does not exist
The evidence you just alluded to suggests that. Furthermore, there is no evidence that will is free - just a compelling intuition that can be and is doubted philosophically by many of a philosophical bent.
and our experiential self both conscious and unconscious says that free will does exist.
That's not good enough. Experience also tells us that the earth is immobile, but with understanding, we can know what we can't sense.
if you are right that we do not have free-will to make decisions, then there is no good reason why we should be held responsible for our actions.
I don't know what you mean by responsible. If you mean punished, then I agree. If you mean forced to make amends or pay restitution, then I disagree.
Assume for the moment that free will is an illusion. How would knowing that change how we should live individually and as a species? I've said several times that I question the existence of just about everything but my conscious experience including my interpretation of what it represents, but that this is only philosophical doubt, meaning understood but not felt as doubt, and as such changes absolutely nothing for me.
I live as if my will were free knowing that it might not be and in fact probably isn't, and Iive as if the outside world exists as it appears knowing that it might not be. Although he may have trouble wrapping his head around them, there is no reason once he does for the critical thinker to resist these ideas. He can't refute them and they demand nothing of him.