Cancer: does any/minimal lymph node involvement always mean cancer has metastasized?

Yes: The presence of any cells within a lymph node associated with a primary tumor means metastasis. Frequently when sentinel nodes are removed to evaluate whether a tumor such as breast or melanoma has spread, normal appearing nodes are sampled but on microscopic exam reveal the presence of tumor cells. This does in actuality represent metastasis at an early stage before growth of the tumor cells.

That depends on: what you mean. Hodgkins lymphoma or non- Hodgkins lymphoma start in lymph system. If there is cancer found in a lymph node (& not a lymphatic cancer) then it is metastatic from where it originated. But having a painful or swollen lymph doesn't automatically mean that there is cancer in that particular node. It needs to be tested to know.