Corrections first: "Can you please explain the adverb 'admittedly'? What does it mean and how can I use it? How many meanings does it have?" This is a simple as looking in a dictionary: http://www.thefreedictionary.com/admittedly For your second question, another online search helps us: https://answers.yahoo.com/question/index?qid=20060814004344AAUnvoK

'Out of one's mind' means behaving crazily or irrationally. "Wow! I put my hat in the fridge! I must be out of my mind after all that studying" We use admittedly when we acknowledge something we are ashamed of, or which is counter to our main argument. "I am quite a good cook, although admittedly I always cook the same dish" "Is Australia a racist country?" "Most people are not racist, though admittedly there is quite a bit of racism."