Does sperm carry cancer cells?

No. No, sperm carry very limited amounts of information, specifically genetic information. Sperm does not carry cancer cells.
Not contagious. Cancer is not contagious, except amongst identical twins, and even then it's hard to transmit. A man with prostate cancer might have a rare cancer cell in his sperm.
No. It is very hard to get anyone else's cancer. Some very inbred populations (tasmanian devils) have a transmissible cancer, but there's none in human beings. One AIDS patient died of his tapeworm's cancer. However... No wife's cancer has ever been found that bears the genetic signature of the husband.