google search – Schema Markup for Web Application Pages and Landing Pages

I have build a Web Application and the website is set-up like this:

  1. Landing Pages that consists of Home, Price, Features and Contact Us
  2. Web Application pages that are for logged in users and only the Login page and Register page can be accessed by Search Engine bots.

At the moment, I have the following schema microdata for all pages, including the landing pages as well as the web application pages:

<body itemscope itemtype="http://schema.org/WebApplication"">
  <meta itemprop="name" content="Awesome Education App">
  <meta itemprop="about" content="Education App for smart people.">
  <meta itemprop="applicationCategory" content="EducationApplication">
  <meta itemprop="author" content="Mr Smith">
  <meta itemprop="creator" content="Example Company">
  <meta itemprop="country" content="Australia">
  <span itemprop="offers" itemscope itemtype="http://schema.org/Offer">
    <meta itemprop="price" content="5.00" />
    <meta itemprop="priceCurrency" content="AUD" />
    <link itemprop="availability" href="http://schema.org/InStock" />
  </span>
  <meta itemprop="keywords" name="keywords" content="education app, etc, etc">

  <ul itemscope itemtype="http://schema.org/SiteNavigationElement">
     <li><a href="home">Home</a></li>
     <li><a href="price">Price</a></li>
     <li><a href="features">Features</a></li>
     <li><a href="contact-us">Contact Us</a></li>
     <li><a href="web-app/login">Login</a></li>
     <li><a href="web-app/register">Register</a></li>
 </ul>    
</body>

My questions are:

1) Do I have separate schema for Landing Pages and the App Pages? I mean have something like this:

Have this Schema for Landing Page, Price Page and Features page like this:

<body itemscope itemtype="http://schema.org/WebPage">
...
<body>

Have this Schema for all App Pages:

<body itemscope itemtype="http://schema.org/WebApplication">
...
<body>

2) Do I add schema for offer, about etc in each individual pages (such as: itemprop="price" in Price page and itemprop="about" in Features page) or can I have all data in every pages like my example above?

3) The App I have created is an education app. Can I use applicationCategory schema like this or is this invalid. If it is invalid, what will be the best category in this case:

<meta itemprop="applicationCategory" content="EducationApplication">

4) Can I use SiteNavigationElement with WebApplication schema type?

5) Lastly, with the SiteNavigationElement for menu items, is my example method correctly implemented or do I need add itemprop for each individual menu items?

Thank you so much for your help.