So say I have a new "simple" web app idea and it somehow becomes very popular after days of its launch.
I don't have the funding to make an iPhone app of the site and someone makes one before I do. What are the chances of this happening? And what can I do about it before and after?
At the end of the day there isn't anything you can do to stop this. If you think your idea would make a valuable/popular iPhone application, it may be worth holding off on the website launch until you have the funds to get an application developed. It depends on the app.
There's not much you can do to keep someone from taking your idea and recreating it if it is basic. If you can patent your software that would help, but that is very difficult to do, and for simple software it's about impossible.
With a good copyright and possibly some trademarks you can keep the entirety of your app from being stolen. If someone wants to just take the time to recreate your app with their own design for another device, there's not much you can do.
You need to see if you can create a sustainable competitive advantage. You can do this in other ways than just writing the code. Even if you do write an iPhone app, there's nothing to stop anyone copying it unless you have some other strategies in place.
I just wrote an extended answer on how you can create a sustainable competitive advantage here :