Are there any royalties or extra fees I'll have to pay if I use Unity iPhone or do I only have to pay the initial license fee?
When developing for PC, Mac, iPhone or Android (in near future) you just pay for the Unity licence (or nothing if you're using the basic version that's free). If you're developing for Wii (and near future PS3, and maybe XBox 360) it will be another story.
Notice that with the exception of mac/pc standalones and webplayers, the platform manufacturers do take a cut of your earnings.
I don't see any royalties in the Unity Licenses. And you only have to buy the Pro version if your company makes over $100,000 in revenue.