I have just found out the person who I have been massaging for years has squamous cell carcinoma, could I have this also under my nails?

No. You do not have to worry about squamous cell carcinoma just because one of your massage clients has been diagnosed with it. If you're concerned get a full body skin exam from your physician.
No. Squamous cell carcinoma is not contagious. It's not possible to get it from direct contact.
Not exactly... Though you may have trapped skin cells under your fingernails, you cannot contract skin cancer from them.
1. There is no medical evidence or mechanism of injury from the transmission of squamous cell carcinoma by either casual or prologed contact exposure. The source for the squamous cell cancer in the masseuse is from prolonged exposure to ionizing radiation and it is purely a local phenomenon not able to cross over to any personal contacts. Continue to enjoy the massage /jmmr.
No. You cannot get cancer just from touching or massaging someone that has squamous cell carcinoma.