You can't liberate a CS that you conquered; you can liberate CSs that another civ conquered (other than CSs that were diplo married by Austria or bought with a Great Merchant of Venice).
To make a great work, the Great Writer or Artist has to be in a city center tile or in one of the six tiles immediately adjacent to the city center tile AND you need an open Great Work slot of the right type -- writing, art or artifact, music. You can't put a Great Work of Art in a writing slot. For example, your palace provides one Great Work of Art slot, but it is often difficult to find more slots for Great Works of Art in the early to middle part of the game unless you are able to buy Cathedrals with faith. The Parthenon has an art slot, but it comes with a piece of artwork, so that's no help in generating free art slots. Great Works of Writing are usually easier, since you just have to build a amphitheater or two (or finish the Great Library) to have writing slots.
To make a great work, the Great Writer or Artist has to be in a city center tile or in one of the six tiles immediately adjacent to the city center tile AND you need an open Great Work slot of the right type -- writing, art or artifact, music. You can't put a Great Work of Art in a writing slot. For example, your palace provides one Great Work of Art slot, but it is often difficult to find more slots for Great Works of Art in the early to middle part of the game unless you are able to buy Cathedrals with faith. The Parthenon has an art slot, but it comes with a piece of artwork, so that's no help in generating free art slots. Great Works of Writing are usually easier, since you just have to build a amphitheater or two (or finish the Great Library) to have writing slots.