Is it possible to have several palpable bilateral supraclavicular lymph nodes and not be related to cancer?

Yes. There are: Indeed many causes of benign, or at least not malignant nodes. Sarcoid is a common one, but drug reactions, infections, tb, HIV are some of a long list of others.

Yes: Several bilateral enlarged nodes in the neck are more likely to be due to infection, locally or systemically. However, enlarged nodes may be due to lymphoma/leukemia and metastatic tumors. If the enlargement has persisted more than a few days, consult your doctor for a more detailed examination and investigation.