In terms of nature and severity of behaviour - what role or variance can be accounted by gender - i.e. predict and/or conclude or warrant a typology of behaivours?
I think the key to answering this question is to look at the socialization process that boys and girls experience. Boys are taught to value being aggressive, risk taking, and even some delinquent behavior is deemed a right of passage (standing up for your self means being able to fight), while girls are conditioned to be more passive, follow the rules, not to embarrass the family, etc (act like a lady). The socialization and conditioning permeates our society and contributes to this gender difference.
Yes, you are correct in terms of socialization - perhaps another key is to explore the various levels/kinds of socialization within the envrionment - in terms of early exposure and saliency of the behaviour
Yes, socialization process could explain the clasical gender differences in aggressive behavior but nowadays, this coud be true in conflicts between a boy and a girl but not in same-sex aggression. My personal perception is aggression between girls are increasingly similar to aggresion between boys. This could be also due to the fact that girls could have asumed (and consequently, identificated with) male patterns of social dominance.
Are they any psychological and developmental factors that could also explain and account for variance in gender difference. Socialization is a factor but are they any developmental factors also?
You should also look at the evolutionary psychology research for genetic factors. Males in all cultures and across species are higher in physical aggression and risk-taking than females. An evolutionary psychologist would have a different take on it. And even socialization begs the ultimate causal question. Don't be too narrow and only focus on "nurture" when nature and nurture virtually always interact to produce such differences.