I'll try to answer your questions

> Who did the Ottoman Public believe to be responsible for the war? What was their opinion on it?

Overall public opinion of the war was unenthusiastic to say the least. While at first the public was angry especially at Britain for seizing two battleships ordered by the Ottoman government via public fundings, they didn't want to go to war for it. When mobilization order was issued, fear, worry and anxiety were the predominant mood throughout the empire. To quote Yervant Odian:

Those drummers (government officials sent to mobilize the men) had become the bane of the lives of all the men of military age, and for their parents too. At all hours of the day, even at night, the ominous sound of the drums could suddenly be heard. Everyone, trembling with fear, would rush to the windows to listen.

I don't know about who the Ottoman public thought is responsible for the war, but unionist propaganda presses blamed the Russians for "attacking" the Ottoman navy during an exercise and brought an unwanted conflict upon the Empire. I don't know how much the Ottoman public bought it though

> Had the Ottomans ever demonized Nicholas II or anyone else in an attempt to encourage public support of the war?

I don't know about WWI, but the Ottoman press had certainly demonized Nicholas II before, especially during the threat of the Russian occupation and invasion of Iran in 1909. Mostly they demonize Nicholas as a brutal dictator and bringer of death. Some examples: https://imgur.com/a/76gCUY6

> What did the Ottomans do when Russia fell apart?

They recaptured provinces taken by the Russians earlier in the war like Trabzon and Erzincan, and launched an offensive to the Caucasus which was moderately successful, marched as far as Petrovsk on October 28, 1918

>How often were soilders allowed to pray whilst on the field?

I don't know the details but generally Ottoman soldiers were allowed to pray with their battalion prayer leaders before going into battle or whenever possible, as routine religious obligations were observed in the military, even during fighting.

Sources:

"When the War Came Home, The Ottomans’ Great War and the Devastation of an Empire" by Yiğit Akın

"The Ottoman Mobilization of Manpower in the First World War" by Mehmet Beşikçi

"Image and Imperialism in The Ottoman Revolutionary Era" by Palmira Brumett

"Ordered to Die: A History of the Ottoman Army in the First World War" by Edward Erickson