Actress_06,
Ugg-A-Wug is a musical number celebrating the Lost Boys and the Indians becoming friends. It's in no way ABOUT indians.
Mysterious Lady, yes, is a fun number, but is very unneseccary. It adds nothing to the plot. In the Rigby/McCoy production, cutting this song and extending Ugg-A-Wugg was one of the highlights of the show. Patti Columbo's choreography made it work one step further by making it a STOMP-style number.
Also, the "Mermaid Lagoon" addition is a GREAT way to end the second act. It showcases the mermaids, it adds suspense, it gives the opportunity for a "pre-game" swordfight, and it delivers the line "To Die Would Be An Awfully Big Adventure" in such a great way!
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle