Which gender has the stuttering genetic strait that can be passed on to their children?

Hard to predict. As genetic research of stuttering is only in its infancy it is hard to predict which gender has more chance of transmitting the gene. But as a rule of thump the sex that suffers less tends to be a bigger carrier, but it may or may not hold true in case of stuttering.
Not known. I am not aware of a sex-linked genetic causality for stuttering, although more men than women stutter. Wikipedia has an accurate entry on stuttering. http://en.wikipedia.org/wiki/stuttering.