Product Mapping and Transition to Agile

Who is responsible for selecting which of the stories are to be delivered per sprint? Is every idea put into the product backlog for prioritization? Who determines how many stories or story points will be delivered each sprint? Who determines if the story or idea is placed in the back log? What is the hardest job for the Product Owner? Is there a way to adapt Scrum Methodology to a standard Project Management ideology? What are the pros and cons of attempting this transition? What is lost in the process of adapting the change? In a group project whereby you have been using Agile / Scrum incremental development processes within the traditional project management as well as working on the same project in the traditional project manner for your project work. What is your opinion of both processes? Do you feel one is better than the other? Elaborate on your decision of which one you think is best.