There's no requirement for applicants to submit anything in writing for the request to meet the definition of an application (verbal applications are still applications).
Application not dated: The loan officer should document the date the application was received. This isn't a requirement of any regulation - just a way to prove you provided disclosures or the AAN in a timely manner. Therefore, you won't find any regulatory reference to support this - either way.
No loan amount:
Again, the loan officer should document what was being requested. If an AAN was completed, that tells me the loan officer knew what was being requested. If there truly was no loan amount, then I would argue you don't have an application. Refer to §202.2(f).
I recommend you check out the webinar I recently conducted for BOL entitled "Applicants and Applications". We go into great detail about what is and is not an application, like the questions you ask. You can find more info here:http://calendar.bollearningconnect.com/main.php?view=event&eventid=1303414477688