I can more easily answer the second question than the first, as I unfortunately don't have any of my references with me.

Yes, the Ottomans did win major battles. Gallipoli itself was a major victory. In Iraq their most significant victory was probably the Siege of Kut, which saw basically the entire 30,000 strong force the British had sent north from Basra killed or captured.

In the Sinai and Palestine campaigns they basically kept the British at a standstill until 1917. They won the First and Second Battle of Gaza which kept the British at bay practically for the rest of the year until the British victory at Beersheba broke the Ottoman defenses at the end of October 1917.

What followed was a year of Ottoman defeats, but nonetheless tough fighting. It wasn't until October 1918 that Damascus was captured (180 miles northeast of Beersheba). Shortly thereafter they signed the armistice ending the war.

Well, sort of. We could then also plausibly count the Turkish War of Independence as a continuation of the conflict, since the fighting was primarily about the Turkish rejection of the settlement that was being forced upon them, though I imagine that's outside the scope of your question.

Ottomans probably fielded around 2.5-3 million soldiers.

And they did much better than people usually give them credit for.

They controlled Azerbaijan and the Caucuses, they controlled Hamadan in Persia, and threatened India.

Also Kut as others have noted and Gallipoli was a big one too.

The Palestinian front stabilized near Lebanon with Allenby’s army going slow.

A few important cities holdout to the very end with years of sieges (Mecca) and the Ottomans only surrendered because Germany signed the armistice.