Can you have non-small and small cell cancer at the same time?

Yes. Non-small cell lung cancer (nsclc) and small cell lung cancer (sclc) are two different types of lung cancer. They can occur together at the same time. Not very common, but it happens. Some of the same chemotherapies (and radiation) may be effective against both types of tumors.
Yes. Specially in the light of a smoking history, dual malignancy have been recorded.