Considering that you are starting in DUS and want to go to southern Germany, I would recommend you start in Cologne (one day should be enough) and then continue your journey along the rhine (take Autobahn A61) and take in the usual sights (Koblenz, the Loreley) which should take a maximum of three days (BTW, you could also do this by train, no need for a car). You can safely omit Frankfurt, as IMHO it's not really worth visiting, and then continue via Heidelberg to the Black Forest. All of this shouldn't take more than one week of your time.

If you want to visit France and Belgium, you should continue your journey back to Düsseldorf via Strasbourg, maybe Metz and then Luxembourg. From there, you could also visit Brussels, Liège and Antwerp (probably not all three as you schedule could get quite packed) and then go back to DUS. Including transfer times, this should be very doable in a 2-weeks-timeframe.

I wouldn't recommend to travel to Bavaria, Salzburg or Austria in general on this trip as this will take you too far away from your departure point (and you'd have to drive more than 1000 km in order to get back, especially the route between the Black Forest and Bavaria (A8) is extremely slow and packed on most days).

As to the B&B, I cannot really help. The only site that comes to my mind is airbnb.com which is actually a couchsurfing community (and probably not what you want). However, especially in the more touristy regions of Germany (which you'll be mostly travelling to) there should not be a problem to organize BnBs "on the fly" unless you are travelling in peak times (at Easter, Whitsun or Labor Day or the many public holidays in June). Oh, and something more - you'll be travelling at a time when most german states, and especially the southern states have summer holidays; thus, it may be good advice to try to book your lodging in advance.