What kinds of apps have you worked on? I'd love to check them out.
The biggest unexpected thing for me was that the simpler you make your app, the more likely people will enjoy it! People always make fun of how the Angry Birds game mechanic is so simple, but that's why it appeals to so many (kids and adults alike). Tiny Piano is dirt simple to play, and that's why users like it.
As developers, we like to always add features. Sometimes, removing features (and making an app simpler) will actually improve the experience.
Regarding IP for the melodies, it is not clear who to contact to arrange a license. Different parties own the copyrights to the lyrics, sheet music, performance, etc. It turns out that my app includes none of those. It just happens to have a collection of notes that, when you tap at the correct tempo/rhythm, sounds very much like a song you may have heard before. ;-)
But really, I try to be a good citizen and link people to the iTunes version of the song so that they can buy it and give money to the artists. With LinkShare, you can even get a 5% commission for each sale you generate. This comes out to about $40 a day of extra revenue for my app.
In the end, if the app becomes super successful (> 100 million DLs), I'm sure the appropriate parties will contact me, and I'll be happy to make a deal with them then!