What are the criteria for determining malignancy in melanoma? Aren't all melanoma malignant?

Yes. All melanomas are considered malignant however they have different levels of metastatic potential. This means that some melanomas have the ability to spread to other parts of the body while others, especially in situ melanomas, have little or no risk of metastasis.
Generally yes. Generally all melanomas are considered malignant. Some would argue that a melanoma in situ (or extremely thin) may be the closest thing to a "non-malignant melanoma". The tumor depth is the most important criterion. Other important ones include lymph node involvement, ulceration, and if the melanoma cells are actively dividing under the microscope.