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.