http://www.labnol.org/software/ipad-pdf-reader-apps/13807/
Update: I can't find any PDF component/library for iOS, which doesn't surprise me. So here's a crazy alternative (so crazy it just might work): Write your app in C#/.Net using MonoTouch, and incorporate the free .Net library iTextSharp. I have no idea if this would work or not.
Another idea might be to incorporate a web service (running on a server somewhere) that will convert your PDF into HTML for you. Your server component can be written in any language, which expands your PDF-component options considerably. And the things you want to do in your bullet points would be a lot easier to implement yourself with HTML.