Should the product owner ideally be as part of the product management team? How does one handle the internal stakeholding if the product owner is outside the product management team?
We had problems since the product owner was not part of the product management team and there were lot of conflicts.
Ideally you want the product owner to be the person who signs off on the final product. They should be either the client you're selling the product to, or, if that's not possible, the final person who is selling the product to the customer. The idea is that this person knows what the final product should be and can guide it's development from afar by ranking user stories and providing feedback at the end of sprints.
Of course, sometimes you can't/don't want to give the customer the ability to see what you're making as you're making it, so you'll have to find a product owner that fits your team's needs. I've worked in both situations and honestly, having someone who knows how to rank features and be a good product owner is often more helpful than having the customer do it, as the customer tends to make everything super high priority, and doesn't understand how software development works well enough to know time estimation.
Agile is more of a brand then a methodology, which type do you mean in particular?
In scrum for example, yes, it would be common to map a previous project manager to a product owner. Although much of the responsibility of the project managing would fall to the scrum master and the team, the skill set required to be a PO (communicating the customers needs, managing customer expectations, directing team efforts towards business value and being the guy who's accountable) are close to those of a PM. However, it is also possible to have a more technical PO or one that more directly represents the customer.
Here's the thing though. The fact you have product management team to conflict suggests that that text above isn't really relevant, because you may be doing cargo cult agile, with the PM and the PO replicating each others work. Do you still have a traditional project manager for example?
