I have no idea about (2) -- try calling the consulate and ask! -- but as for (1):
In order to get the Belgian consulate to process a visa application, you need to propose an itinerary where Belgium is the main destination of your trip, which means it has to be the state where you will spend most of the time (15 versus 7 days ought to do it). If they issue you a visa, you need to (intend to) follow that itinerary at least roughly, or you'd be guilty of visa fraud, which is grounds for canceling the visa.
A visa issued by Belgium is valid for entering the Schengen area at Frankfurt in order to proceed to Belgium later. This is not even unusual, since Frankfurt is one of the most well-connected airports in continental Europe.
However, if the border guards in Frankfurt suspect that your true intentions do not involve going to Belgium as a main destination, you may be pulled aside for further questioning where they try to verify your story. So you should be prepared to offer details of your itinerary, ideally with bookings for your travel from Germany to Belgium, hotel reservations, some concrete idea what you're going to do with yourself for 15 days in Belgium (which is not a large country), and so forth.
If the border guard knows of your canceled appointment with the German consulate, that would certainly tend to make him suspicious. I have no idea whether the German authorities share enough information internally to make this relevant, but based on the risk alone, you ought to make an effort to have solid documentation with you when you arrive. (For example, don't plan to hitch-hike to Belgium and find a vacant B&B room when you arrive).
Oh, and try to come up with a better reason to want to go to Belgium than "it's all the same to me".