Is it possible to store all records of the news extension (ext:news) on the same storage page, but show only records, which are created by the loggedin backend user?
So the current backend user can just see and edit his own records? Admins should see all records of course.
No, this is not possible, since backend user permissions on record level are not implemented in TYPO3.
So you either have to separate the news records of the users in separate sysfolders or you could try to use hooks (e.g. $GLOBALS['TYPO3_CONF_VARS']['SC_OPTIONS']['typo3/class.db_list_extra.inc']['getTable']) or XClass to customize TYPO3 backend to your needs. I do not recommend the latter, since the TYPO3 backend permission system is complex and you would need to make sure to restrict record access in several parts of TYPO3 (e.g. recordlist, element browser, related news field, ...)