There are several topics that I offhand recall having seen in Igrot Moshe, but I have a tough time locating them.
Is there a topic index, or even better an online search that I can do to locate specific topics in Igrot Moshe?
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There is a very popular sefer called Yad Moshe which is an index for Igros Moshe. See here.
Yad Moshe, the classic index to Igrot Moshe, authored by Daniel Eidensohn now exists in English. It is printed on demand so shouldn't get out of stock.
Here is a sample picture