Xcode allows Mac OS X and iOS development for free. It's a public download on the App store.
To distribute apps through the Mac App store, or the iTunes App Store there is a $99 a year developer fee which includes the certificates needed to run your app on other people's computers or iOS devices.
So on a Mac yes, completely free to make apps for your own desktop. (Because you're bypassing binary signing, which is optional on a Mac) On iOS you will only be able to use the simulator until you pay for a dev certificate. This is because of no "side loading".
Now there is a free developer account which gives access to documentation and sample code (and old WWDC videos?), much of which is google accessible but some of which is not. Kids can get the free developer accounts, practice on a simulator and apply to go to WWDC for free (https://developer.apple.com/wwdc/students/).
So long story short. Things are not that simple, it's a nuanced situation, but YES you can start coding iOS apps before you're 18.
The WWDC app requires a dev account because that's pre-release info that requires signing an NDA. That would normally exclude minors, but it works the same way as kids going to WWDC, via sharing a dev account with their parent or guardian. So a grown up gets a dev account, puts in info that it's for their minor child... pays for a dev certificate and a kid can make their own iPhone apps with parent's permission.