Creating strategy game using OSM

Hello! Me and my friends would like to create private simulation game based on the OSM map.

The game would be working on internet domain, but would be only accessible by password. The question is, is it possible to import the map to another webpage, and if is, how? Also when starting to create the game, is it possible that we would accidentally edit the public map, and if is, how do we prevent doing that? If the internet game would be hard to create, is there better ways then? For ex. based on game engine or other?

So if i explain a bit more about the game. The game itself is kind of emergency response centre simulation game based in Finland, and would be multiplayer game. We are not interested touching the map it self and we would keep the game 2D. The players mission is to dispatch a vehicle to accident and select appropriate vehicles to move from point A to point B, and vehicles would use roads, water or ”air” depending which kind of vehicle(s) would be dispatched to scene. And after the situation would be resolved, the vehicle would get back to its main station or hospital or whatever would be its destination afterwards. As i said, the game would be multiplayer and should be ”realtime” on all of the players at the same time, is this possible using OSM as the base map?

Thank you