如果在应用页面上发布帖子，用户会在墙上看到帖子

Question

I would like to know, if a post is made by an app on a page which is associated with the app, then the posts published on that page will be shown on users wall or not, provided that users have allowed access to that app.

Answer 1

No, users of your applications who are not fans of associated page will not get posts published on that page appears on their wall (associated page it's still a page, nothing unusual here).

You can place Like Box social plugin in your application so your users will be able to like associated page and get subscribed on updates.