While having these groups kept under the same country rule may make them easier to track and understand, forcing two countries would only lead to further internal problems and only compound the problems we have seen. We have to try and stem the problems which lead to these insurgent factions in the first place.
No, despite all of the international sanctions on Iran, they are still a fully functioning country with a government and fairly unified military force. Iraq is on the brink of civil war because of a Shia dominated government and a Sunni group that feels left out of the political process. Iran and Iraq are two entirely different countries that have limited similarities at this point.
No, Iraq and Iran should not become one country, because Iran would end up oppressing Iraq, and it would all become very radical. There are a surprising number of people in Iraq who want to live as a free people in a Western culture. If Iraq and Iran were one country, they would have no chance of that.
I believe Iraq and Iran becoming a unified country is a possibility but rather it should happen really depends on the people that inhabit both Iraq and Iran. I do not believe this is a decision outsiders should make or even suggest. Countries evolve and change and Iraq has been in this process of change for many years now. It's difficult to say where they will land.