You can avoid toll roads if you drive north to thr Netherlands, and then head east into Germany. German Autobahns are toll-free for private cars; only trucks have to pay toll. You won't even hit France.
The LEGAL speed limits vary, and the signs will tell you. If there is no speed limit announced, it is 110 km/h in Belgium and the Netherlands (upper speed limit); in Germany, when there is nothing else announced, the RECOMMENDED speed is 130 km/h. You can drive faster where allowed, but German highway police is strong on tailgating, so keep your distance. They have cars faster than yours, and if you see the sign "POLIZEI - FOLGEN" do what it says: Follow, and stop BEHIND them. They're usually friendly, but even if you don't see them, they DO have guns.
From Brussels to Berlin, in my experience, you should plan an overnight stay somewhere in between. I drove from Bavaria to Amsterdam once, that's about 1.100 kilometers, and it took me 13 hours speeding like hell, and I wouldn't do it again. Brussels-Berlin is a bit shorter, 950 maybe, but if you don't take your time, you miss so many beautiful things on the way that are worth seeing. If you haven't got the time for a 4-day ride, I'd rather recommend you take a plane. It's less than an hour, and less of an experience.
I'm sorry, Mr Bahnhofsklo, the difference between Google Maps and driving is that I DID IT, and you have to use a Klo (a loo) now and then and also get hungry now and then, so you takea detour. And with all the construction areas and trafficjams in summer, you DEFINITELY won't make it from Amsterdam to Berlin in a day.