I have installed Umbraco 7 in MVC application. Have you achieved ever rendering MVC View from Surface Controller ? If it is possible to do how it can be done by passing model and passing a query string parameter to View ?
If I understand your question correctly, you need to use an approach called Route Hijacking, rather than surface controllers.
Simplified, the steps are:
In your view / template, you will then be able to use
@model MyNewModel
instead of
@inherits Umbraco.Web.Mvc.UmbracoTemplatePage
Here is a very good tutorial / explanation on the approach.
Be sure to read the follow up post too