Running Navision RTC through the web (LAN & IE)

As far as I know you can't. I'm not sure why you would want to either, not over a LAN. You can use webservices to expose functions and data, but not to see the RTC in IE. The RTC needs to be installed on the client machine. You might be able to use the RTC to connect over a WAN using VPN, but you would have to check performance for that.

in this world there are x kinds of applications. We'll discuss 2 here.
First the webapplication. This application can be run from any browsers and is not standalone. These applications have code in a scripting language (usually javascript) with some html and css for layout. This is an application that can be used on any OS that has 1 or many browsers. Some applications are dependend on third party software. Which can be extensions in a browser (like flash and silverlight).

The other one is the standalone program. this is usually developped for 1 platform and doesn't need a browser do run.
It has it's own rules for displaying and handling data. And even can take up your entire screen. It's not depending on a browser and can't be run with it.

Dynamics Nav is the latter, so you can't display the RTC trought IE.

Just a quick question, are you developping for fun, training, ordered by customer, ...?