Well I finally figured it out. As I understand, my question had been read for 196 times, yet nobody seemed to know how to help me any further (to put it friendly) or maybe no-one even bothered to give any reply. Both suggestions I find hard to believe, but are nevertheless pretty disappointing to me... Also, considdering the fact that I'm pretty sure that at least one or two Falkenburg-mod players must have seen this post, why not trying to help me out here? Correct me if I'm wrong, but isn't this forum all about helping each other with their questions and problems?
Anyway, by watching many, many movies of the Falkenburg-mod on YouTube now, I finally stumbled on the one that showed me how to really activate the game, like I asked you guys about. For those of you, who really could not help me out with my question, here is the answer:
When the game starts, you immediately see the firehouse. On the firehouse terrain, near the adjacent building, you can see a fireman just standing there in front of a metal fence/barrier. You then have to rightclick on the fireman to make his "function menu" visible. Apparently, once you click on the glove in the "function menu", the game is activated and you can start playing the game, since immediately afther clicking the glove, the first emergency call is placed.
Well then, this post - for what its worth...