Which is the maximum number of players, that can be in the game in the same time?
From what I have read Elite Dangerous will use different instances. And each instance can hold up to 32 players.
Remember that instances are basically a bubble around your ship that is defined by your scanner/visual range. Although the size is somewhat adaptable. This means that there can be players in one instance and another group of players in another instance some distance away. If one player from the first instance starts to travel towards the seconds instance the players in the first instance will eventually drop of his radar due to distance and the other players will eventually come into view. So if the system works as intended this will feel seamless from the players point of view.
And it will be heavily instance in that regard. There might be hundreds, if not thousands of players in your vicinity at any one time but you will only ever see 31 other human players plus AI pilots. This might change as FD make further improvements to the networking model.