Q:

Post on user's wall with the Application

Is there any way to post on user's wall as the Application and not as user?

A:

It's hard to provide a definitive answer without some more context as to what sort of post you want to do, but the answer is probably no. 
We dont provide a a mechanism for pages or applications to write on a users wall directly. 
As a Page, you can post on your wall, and the messages you write will be shown to a subset of the users who have liked your page in the news feed. 
As an application you can use stream.publish to post on the users wall/timeline with an application attribution. But it's not as the application per se. 
With Timeline Apps you can use the Open Graph to publish actions the user has taken with your app, like Spotify does. So you're posting what the user has done with your app, rather than posting as the user. 
HTH

