Yes
Yes they did. http://www.pillow.co.uk/anzac-day.html
ANZAC troops fought at Gallipoli between April and December of 1915. Later the Corps was disbanded and became the NZEF (New Zealand Expeditionary Force) and the AIF (Australian Infantry Force) and fought in France and Belgium with distinction. New Zealand troops were undefeated on the Western Front until Passchendaele in October of 1917.
Not under the term "ANZAC" they didn't. New Zealand became the NZEF (New Zealand Expeditionary Force) and Australia became the AIF (Australian Infantry Force).
The United States' troops fought on the Western Front in France.
A battle that the original Anzac fought in was the Turkish Attack at Anzac Cove. This battle took place in 1915 with the attempt was for the Turkish to take over Anzac Cove and force the Anzac out to sea.
On June 26, 1917, the first US troops arrived in France during World War I. Unfortunately, the soldiers arrived untrained, and lacking in both equipment and readiness to begin to fight on the western front.
To England for training, then on to France and the Western Front.
Russia's withdrawal from the war allowed Germans to move thousands of troops from the Eastern Front to the Western Front in France.
The Gallipoli campaign was Winston Churchill's brainchild. It was supposed to be a diversion from the stalemate on the Western Front. The troops were supposed to force their way through to Constantinople (now known as Istanbul). I don't know whether after that they were supposed to flank the Germans on the Western Front, or just scare the Germans into submission. They never made it.
The soldiers were forced to fight in Gallipoli Western Front and Middle East
In 1915 they fought on the Gallipoli Peninsula in the Ottoman Empire (modern day Turkey). After that they split into two forces; the infantry formed the NZEF and the AIF and went to the Western Front while the cavalry and mounted riflemen from New Zealand and Australia fought in the desert at Palestine.
The enemy of the ANZAC (Australian and New Zealand Army Corps) during World War I primarily consisted of the Ottoman Empire, particularly during the Gallipoli Campaign in 1915. The ANZAC forces faced fierce resistance from Ottoman troops, who were defending their territory. Additionally, during other campaigns, the ANZACs also fought against German and Austro-Hungarian forces on the Western Front.