Personally, I think that most of the Middle East to its south is a lost cause. They're going to have to deal with Arab nationalism sooner or later, and European powers, at the very least, a European Power, will use the Arabs to achieve their own ends in the Mideast. It's often said that after oil is discovered in the Mideast, Ottomans are going to be rich and possibly powers again, but frankly, I think that after factoring in European powers, the oil will simply become a resource curse for whoever owns it.
Having said that, I believe that none of this precludes an Ottoman Empire surviving into modern times. Specifically, I mean a Turkey ruled by an Ottoman Sultan, mostly unopposed.
I don't believe that the Middle East is a lost cause for the Ottoman Empire. Arab nationalism was limited to a small group of mainly Christian and Egyptian intellectuals until after the fall of the Ottoman Empire. The Ottoman Empire offered a credible alternative to Arab Nationalism (mainly, Islamic nationalism/Islamism) so unless this ceased to be a factor, I have difficulty seeing how Arab nationalism could over-take it at all. The Arabs will still be more willing to side with their Ottoman Caliph than the Europeans oppressing other Arabs in North Africa, so encouraging division to seek control of oil doesn't make any sense.
Much more likely, the Europeans will prefer to work with the Ottoman Empire at extracting the oil fairly easily. Its not exactly as if the Ottomans would forbid European companies from operating in the Empire, though their privileges may be curbed during WW1.
As to answer the rest of the OP's question, relations are likely to be vastly changed. Non-Muslim minorities had declared equality since the 1830's (and actual legal equality since the 1850's), but the Ottoman Empire still suffered from occasional bouts of communal violence, usually resulting from Christians seeking more power and autonomy locally) which increased after the independence of Bulgaria. The question is what happens to the Armenians. If the Ottomans stay out of World War One, they may not bid for independence after all, but they will continue to be a problem for the Ottoman government until Russia's government collapses (which may be delayed if the Ottomans are neutral, or even butterflied). The position of the Jews will be improved compared to their position today in the Middle East, but there will be no Israel, and only limited Jewish settlement in Palestine. The Ottoman sultans had rejected Zionist offers to pay their debt in return for Palestine on a matter of principle, so the chances of them agreeing later on are small as well. The Sultans are likely to allow some immigration in order to stimulate the underdeveloped local economy, but not too many.
As for Kurds, their status will be interlinked with that of the Armenians. As long as they are still around in significant numbers, the Empire will likely play one off against the other (the Kurds had been troublesome sometimes for the Ottoman Empire for non-Nationalist reasons, but unlike the Armenians, could be appealed to on religious grounds).
