It looks very similar, but keep in mind that ' ŝ ' is a completely separate letter in the Esperanto dictionary and sounds like (sh).
"mouse" is "muso".
"fly" as a creature is "muŝo".
http://esperanto-panorama.net/vortaro/eoen.htm So, in this dictionary "musz" if it existed, would come before "muŝa".
Enjoy the alphabet song in Esperanto: http://www.bing.com/videos/search?q=esperanto+alphabet+song
"moose" is "alko", and that is not so far off when you realize that in Europe a "moose" is called an "elk". http://www.majstro.com/Web/Majstro/bdict.php?gebrTaal=eng&bronTaal=eng&doelTaal=epo&vk=0&teVertalen=moose
Yes, it is the diminutive form of the word fly from latin.
That actually does make sense as "insect" is one of the meanings of "mushi" in Japanese. It's a "Small World After ALL!" http://www.kanjijapanese.com/en/dictionary-japanese-english/mushi