It is my understanding that dowries were expected and sometimes legally required in the medieval period, but modern Europeans no longer hold this custom. When and why did this change happen?
Add-on question: Is the tradition that the bride's parents pay for the wedding related to the dowry tradition?
Sorry for the short answer, but all your answers can be found in the article "From Brideprice to Dowry in Mediterranean Europe" by Diane Owen Hughs. One of those articles that never goes out of style.
edit: it doesn't talk about how the dowry was phased out, but it would answer a lot of your questions.