Now, in terms of circles of knowers, I'm pretty far removed from these conflicts, though I know there are Diploma Programme IB students at Poudre who are quite close.
Nevertheless, these are my ideas about how some of them might be resolved, or simply my opinions on what would be most just:
Israel/Palestine: Either allow the formation of a Palestinian state from the West Bank and the Gaza Strip, put the region under control of the UN with input from both Israeli and Palestinian leaders, or eliminate the West Bank and Gaza Strip zones and incorporate the country under joint leadership, perhaps with a legislature composed half of Palestinians and half of Israelis and two prime ministers.
Iraq: The US needs to withdraw its troops, if not immediately definitely within a year or a year and a half. I'm also aware that there are conflicts between Shiite (Sh'ia) and Sunni Muslims as well as the Kurds. So far as I can tell, one of the main conflicts is that the plurality of the population is Shiite, so the Sunnis (who were in control prior to the US-led invasion) are concerned that a Shiite majority in the legislature will lead to the government ignoring the needs of Sunni Iraqis. The Kurds, on the other hand, want their independence, though I'm not clear on why it is denied them. I think the best solution seems to give the Kurds their independence (if this means taking territory containing a Kurdish majority from other countries to the north of Iraq do so). The Sunnis can either form their own government or join neighbouring Saudi Arabia (as I understand natural and economic resources are scarce in central Iraq, which is primarily populated by Sunnis). The Shiites can choose a new capital and form their own government in the South (primarily populated by Shiites). The other option is to either stick with the current government and try to even out the majorities either with or without the Kurds.
Disclaimer: these are to an extent just ramblings. As I said before, I am not very close to the issues mentioned here at all, and don't mean to offend anyone. Those who are more informed that I (Karam? Meredith?), please shed some more light on the issues and let us know how you think they might be resolved.