Do children only have the rights to their parents inheritance when both pass away, is there any difference if they are not children from both parents, as well I was told that daughters have a equal right is that correct?

When a father departs from this world his sons inherit him, while the mother - his wife collects her Ktubah from the inheritance. When a wife passes away her husband inherits her. Only biological children inherit. According to the basic law daughters do not inherit among sons, nevertheless the Rabbis instituted as one of the conditions of the Ktubah that when a father dies the daughters are supported from the father’s estate until they get married or until they mature. What is left is given to the sons. Even if nothing will be left for the sons, the daughters have precedence. There are many details to these laws; they also depend on the law of the country and other factors, so it is recommended to consult with a Rabbi or a Rabbinical judge in each specific case.