I have a .NET application in which most of the UI is custom. On some of the pages, I am using ExtJS4 components, such as Grid, to display a table of Users for example. I a
The latest version of Sencha Cmd explicitly supports multi-page application development and deployment. If your dependencies are set up properly it allows you to create page-specific build packages to optimize loading and caching per page. Although from a practical standpoint, if the amount of overlapping code is large enough (and/or the total amount of code small enough) it might be better to KISS and just include all of your app classes in one file.
Yes, each page that uses Ext should typically use either Ext.onReady or Ext.application wrapping the app code. Whether or not you follow the MVC pattern is up to you and should be driven by your app's requirements and complexity. For simple cases it's often not merited, but for complex apps or team development it probably makes sense to follow MVC.