Basicly, i want to provide users to share my application's android market url. I do not want to use "facebook api for android" so my way is like that when the user press the button of "share on facebook", web browser opens "www.facebook.com/sharer.php" then user login it and application's market url string paste in "write something" (textbox of facebook sharer.) Is it possible to make like this or must i use facebook api for this work?
No, not really, unless you really hack things up. Look at the dialogs documentation: http://developers.facebook.com/docs/reference/dialogs/, for each dialog they provide a url, but if you try them you'll see at the bottom of the dialog that it's "shared via Cool Social App".
You need to have an application if you want users to share, and if you already have a fb application, and you want to do the share from an android application, then yes you can just open a web browser with the dialog url, but using the android facebook sdk will be a much better choice since it has the Single Sign-On: http://developers.facebook.com/docs/mobile/android/sso/, that will check if the user is already signed in to facebook in the mobile device, and if so will skip the authentication process.