It depends on what is meant by intervention. We did send troops into Mexico after Mexico raided a town in New Mexico. We had been involved with Mexico forever (at least since the Mexican-American War in the 1840s). Wilson supported various contenders for political power in Mexico. His motives for most diplomatic efforts were as you say, his concept of "moral diplomacy".
Your answer for #2 is spot on! Very good.
1) Why did President Wilson intervene in Mexico?
A: President Wilson intervened in Mexico because he desired to lead by moral example and promote Moral Diplomacy.
2) What incident triggered the beginning of World War I?
A: The assassination of the heir to the Austro-Hungarian throne triggered the beginning of World War I.
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Should I change my answer for #1, then?
Maybe just explain a little further for #1.
yes, I would add to it if I were you. You're not wrong, but there was more to it. Look up Pancho Villa and the Mexican raid on Columbus (Columbia?), New Mexico.
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