HTTP Response/Request Class
I don't quite see the purpose of your class. You are basically taking an existing class from the .NET Framework and wrapping it up in something that only exposes a fraction of the functionality.

The code also relies on a lot of hard-coded settings. While specifying a specific user-agent might not cause too much concern, always using a specific HTTP proxy will.

You provide the results of the request in two ways. The actual HTML is returned as a string from the method (what if the site returns binary content?), while the cookies are set in a property. It's strange to have a class called Request that contains a property starting with Response. The approach taken by the HttpWebRequest is much cleaner as it returns a whole class that contains all the information of the reply.