Web Apps
Web Apps are highly optimized special websites that are accessed from any device but still look and feel like a full-fledged application. An early example would be GMail. Here is an old blog post by jQuery's John Resig on early web app development.
1. Can we create apps more easily and accurately with the help of Javascript?
This is a bit mis-leading as the intents may be different. The goal of web apps to hit the widest possible audience with minimal effort, however, you are restricted to non-native functions.
Native functions include use of the device hardware such as camera, gps, touching other apps, notifications etc. There are several libraries that provide a wrapper around your web app to expose these underlying calls but then you must do that for each device. Libraries include: Phonegap, Titanium.
2. Does Apple approve apps created at least partially with JavaScript?
Most certainly! They even have a special section. With most webapps it is just a bookmarklet the user drags to their home screen for quick access. If you want to do the true app in the store you will need a wrapper library as mentioned before to package your app together.
3. How should one begin learning JavaScript?
Out of scope for this question, but Douglas Crockford is one of the better teachers, he has a multi-part video series as well as a book to get you learning the "good parts".
4. Are there any tutorials that can help me to understand and learn JavaScript, particularly for iPhone/iPad programming?
Honestly, it would best to learn javascript first, as it is a prototypical object based puzzle then worry about how to utilize the various frameworks for best mobile performance.
Adding 5. What are some javascript mobile frameworks?
These are just the most common but I would browse each of them a bit as jQuery, dojo and sencha have different approaches on how javascript should be used.