You've asked a question about mental peace and then counter acted it immediately with "Tell us something abut inner conflict." Anyway, let's have a go at answering the first question.
Mental peace is experienced TOTALLY as absolute silence of the mind. No verbal chatter experienced, no emotional reactions arising. That's how I would describe it. You are an "I am" in awareness with nothing else added.
Of course thoughts arise continually but they are ignored. They are ignored to the point you are no longer aware of them. For you know they are not you. They are a phenomenon of the mind (that nebulous concept, the mind)
But mental peace is -as you would have it - an absence of inner conflict. There is no war going on between the conditioned mind's desires, clingling, or aversion to life AS IT IS at this moment. For example, if you are looking, speechless and in awe at a beautiful sunset, and totally present in that moment, you are in a state of mental peace.
If you are taking note so you can tell someone else about what you experienced, then you are already out of total inner peace. You're not in conflict, but you are 'in your mind' (and probably identifying with it)
Hope this has helped.