Could my nephew have spina bifida if I did?

Unlikely. Spina bifida (there are several types) is associated with some known genetic defects however the majority of cases are spontaneous and most cases are more likely related to folate (folic acid) deficiency during pregnancy. The general answer is that this is unlikely to occur in your nephew.
Unlikely. Most spina bifida does not run, in families, but occasionally does. Depends on type of spina bifida. If the cousin is beyond early childhood and does not have symptoms, then highly unlikely.

Related Questions

Hi, my nephew was born with spina bifida. His bowl and urinary movenents are not intact, no foot reflexes. Is there any way to cure this condition?

no. The damage to the spinal nerves occurred because of a developmental problem. There is no way to reverse this but there are many ways to make this a problem he can live with. Consult pediatric rehabilitation experts. Your pediatric neurosurgeon can direct you. Read more...