I don't have the specifics of TTL's Second Empire completely settled yet, but I'd say Napoleon II's regime is closer to the government his father attempted to establish in the 100 Days, rather than the OTL Second Empire Napoleon III created. As he died relatively young in OTL, I don't have much to base his political beliefs off of for this timeline unfortunately, but he did receive a good - if rather conservative - education while in Austria. ITTL, he escapes his "confinement" and gets a chance to travel and see the world, spending several years in Switzerland and the United Kingdom where he is free to develop his own politic beliefs. Overall, he is definitely a monarchist, but I tend to think of him more as a constitutional monarch rather than an absolute monarch.
The Ottoman Empire is definitely in for a rough time ahead of it, regardless of the outcome of this war. At the end of 1855, they are already taking millions of Pounds in loans from Britain, they've suffered tens of thousands of casualties they didn't take in OTL, and the fighting is predominantly on their territory. They've already agreed to hand over some provinces to Greece, although their loss is lightened due to their general restlessness and poorness, as well as increases in British loans to sooth any rustled feathers in Constantinople. Even if they were to miraculously win the war, they likely wouldn't gain much in terms of meaningful compensation as was largely the case in the OTL Crimean War. If they lose - which is far more likely - then they'll be in an even worse state as at a minimum, they'll lose their control over Wallachia and Moldavia, and they'll probably lose some territory in Eastern Anatolia as well. Anything beyond that is dependent on how well Russia does going forward.
This war will definitely have some lessons to give, particularly the force multipliers that are rifles and percussion shells. There will also be a lot of scrutiny given to poor medical practices and logistical systems implemented on both sides after the war, and for good reason. That being said, I expect the Russians to be less inclined to modernize and reform their military apparatus ITTL, owing to their greater success, while Britain will likely accelerate their OTL reforms in response to their poorer performances.
I realize that I've been trending towards longer updates recently, the last one in particular was the longest yet at 15 pages of text or 8,913 words. My intent was to give you all more to read, but it has been been slowing my release schedule down, unfortunately. So if you all would like, I can definitely break these parts up a bit, giving you all more frequent updates and me more time to focus on other aspects of the timeline.
In terms of battlefield casualties, the British are actually doing quite well after a year of fighting all things considered, but they've been devastated by disease like in OTL, with Cholera and Typhus killing many thousands. Of a prewar total of 150-160k men, around half has been sent to the Balkans, a quarter was in India, and the rest was scattered across the globe in Canada, Australia, New Zealand, South Africa, etc. They do have more men to call upon, but if forced to choose between India and the Ottomans, the British would choose India every time. That being said, the situation in India isn't that dire just yet, so they still have some room to maneuver.
The Ottomans in contrast, are in a very bad way right now. For simplicity's sake I'll say that there were 150-160k Nizamis ITTL at the start of the War in the Spring of 1854, most of which were in the Balkans, although a couple thousand were in the Caucasus at that time and around 200,000 reservists rounding out their armies. By the end of 1855, the Nizamis in Eastern Anatolia have been effectively wiped out, dying either from battle wounds or disease, although many deserted or simply disappeared altogether. Similarly, the number of Nizamis in the Balkans have been more than halved by casualties and illness, forcing the Porte to call upon their reservists to fill their depleted ranks. These troops are more akin to garrison troops, irregulars, or militiamen rather than professional soldiers, so as the war continues and the Ottomans are forced to rely upon these troops more and more, their fighting proficiency will gradually decrease.
Unlike the Ottomans and the British, Russia can replace its lost soldiers with its reserves, but even these are not limitless and can probably continue to fight for another two years or so at its current pace, before their losses really begin impacting their ability to fight. More than likely though, the British and Ottomans will run out of men first so at this point its a war of attrition for them. Not all is going well for Russia, however, as their economy is being destroyed by the British blockade and their minorities are beginning to make some noise, hence the need to push the offensive. There is also their increasingly terrible supply problems as you mentioned, as shortages in weapons and ammunition make it very difficult to effectively wage war.
Cyprus is still a part of the Ottoman Empire at this time, both IOTL and ITTL. The UK wouldn't get a hold of it until the Treaty of Berlin in 1878 and even then, they ruled Cyprus on "behalf" of the Ottoman Government which still held de jure control over the island. They wouldn't control it outright until 1914 when the Ottomans joined World War I against Britain.
Regarding Greece's economy post Great Eurasian War, it will definitely be much stronger once it fully integrates Thessaly, Epirus, the Ionian Islands, and the Dodecanese Islands. The real gain here is Thessaly which has some of the best farmland in all of Greece and will effectively become the breadbasket of the Greek State. The Ionian and Dodecanese Islands also have decent agriculture industries, with Zakynthos being a sizeable producer of currants and Rhodes has a number of famous vineyards, they also have talented sailors and provide Greece with several good ports. Epirus in contrast is rather lackluster, but it does a solid herding industry and there is a small tobacco industry around Ioannina, most importantly, it provides Greece with a defensible Northern border and it gives control over the entire Eastern Ionian Sea.
Well I won't say if Egypt becomes independent as that might spoil my future plans, but it definitely won't become a British protectorate like in OTL.
Very interesting Damian, I'll definitely check out that book when I get the chance. Overall, I haven't decided on the exact details of what the Balkans will look like after this war, but Serbia will definitely be gaining more autonomy regardless of the outcome. As the war continues, the Ottomans will essentially be forced to recall their troops from Serbia, thus necessitating an agreement of some sort to prevent their rebellion and entry into the on Russia's side. While I doubt Serbia would actually declare war, the Ottomans don't know this and more importantly, they're a little short on trust right now after their dealings with Greece and Britain. I definitely agree, though that Russia will be forced to pick and choose between Serbia and Bulgaria as their competing claims will make it impossible for both of them to peacefully coexist.
Greece will provide as much financial and material support that it can to Greek Schools both in Cyprus and the rest of the Ottoman Empire.
By in large, the Greek citizens of the Kingdom of Greece consider themselves to be Hellenes, while those Greeks under Ottoman administration (particularly those in Constantinople, Anatolia, and the Levant) generally consider themselves to be Rhomaioi. That said, I don't think its mutually exclusive as the modern Greeks consider the Rhomaioi to simply be their Medieval ancestors so there is definitely some leeway in regards to the terminology, especially if the Greek state ever recovers Constantinople and reasserts its connections to the Basileia Rhomaion.
Egypt:
The Khedivate of Egypt will be remaining neutral in the current conflict for reasons that will soon be revealed. Hint: It has something to do with Ibrahim Pasha. That said, individual Egyptians and Arabs under Egyptian control have been joining the fight against Russia, albeit somewhere in the range of a few thousand, rather than the 40,000 they provided in OTL. Some of these men are, or rather were Egyptian soldiers, but most are not, meaning they are not as disciplined, nor are they as proficient as the OTL Egyptian contribution to the Crimean War, but at this point the Porte is thankful for every warm body that it can get.
Cyprus:
Regarding the discussion a potential revolt on the island of Cyprus, there probably won't be one during this war as Greece has effectively announced to the world via its agreement with the Porte, that it won't support further Greek partisans in the Ottoman Empire in return the cessation of the Dodecanese Islands in late 1855 and the cessation of Thessaly and Epirus at the end of the War. There is also the matter of the Royal Navy's Mediterranean Squadron which is currently operating out of the Aegean right now and wouldn't look too kindly upon Greece if it attacked their ally during a time of war.
After the war though things are a little different as the Ottoman Empire is in for a tough time ahead of it as a result of the greater financial and military burden it has had to bare ITTL. Greece, in contrast is only getting stronger, with the inclusion of Epirus, Thessaly, the Ionian Islands and the Dodecanese Islands, boosting its population to 2.2 million and strengthening its economy by a great margin, enabling the Greek military to expand accordingly. The Greek navy is particularly important to the Greek state and will likely receive substantial investments in the years ahead, enabling it to go toe to toe with the Ottoman Navy despite their comparatively small size. Whether this would result in a Greek/Cypriot victory over the Ottomans I won't say, but it is interesting to consider right now.