If moles are full of melanin, does that mean an existing mole if exposed to uv radiation won't turn to melanoma?

No, risk remains: 'moles' on the skin are nevi, essentially benign but abnormal collections or growths of melanocytes in the dermis (the layer just under the epidermis) and sometimes also in the epidermis. Uv light damages the dna in cells and when it does so in melanocytes in nevi they may be transformed into melanomas. The pigment does not protect the cells.