Are head/neck squamous cell carcinoma tumors always immobile/rigid? if so, why? if not, how often are they immobile?

I am not sure what kind of squamous cell carcinoma in your question. Is that skin cancer or nasopharyngeal cancer? You probably mean the metastatic lymph nodes not the malignant lesion/tumor by itself. The malignant lesion is fixed, attached to the skin or mucous membrane of the nasopharyngeal area. The sentinel (metastatic) lymph nodes of squamous cell carcinoma are usually mobile at first.