You seem to have two problems here so let's work them out one at a time.

First, you say "image is not visible". Are you talking about your own images
or something you're trying to reference in SharePoint or ...? Quickest thing
to do is to look at the rendered source in the browser (right click, View
Source) of the page of the app. Look for your image and see what the url
it's referencing is.

As for the CSS, the article talks about how to create an application  to run
under the SharePoint context but until you put anything "SharePointy" on the
page (like a SharePoint Web Control) it's just an ASP.NET application so
it's not magically going to use the SharePoint CSS files (if that's what
you're trying to get). Also you'll need to tag your own controls with the
SharePoint class names in order to pick up the styles (after you add the CSS
file to your page).

The ASP.NET application  created by me is separate from SharePoint
Server. The Stand alone ASP.NET application and SharePoint is running
on the same Server.

After installing the SharePoint I found that the ASP.NET Application
is not running. The I have implemented the patch provided by
Microsoft from the following link

support.microsoft.com/default.aspx

Now the ASP.NET application is running  but the images of that
application is not showing. This ASP.NET application has separate CSS
file which has no effect on it too.

At the portion of the image a "CROSS" sign is displayed. I have right
click on that and found the Address [url]
= "http://projectsrv/swa/header.gif" which is correct but the type
and size information of that image is displayed as "Not Available".

The ASP.NET application has not relation to SharePoint except both
SharePoint and the ASP.NET application is running on same physical
SERVER.