1: There is currently no networking in the engine, but it is a planned feature and Spark has already done some work to make it secure by separating bits from other bits. Aru has expressed interest in writing a net library or adapting an open one to Grit, but we haven't spoken in a while so I'm not sure if there is any progress from him.
2: There isn't one programmed now, and it would probably be something someone else would need to add, and even then it may or may not make it into the official builds. It is certainly possible and would be a very great addition to the engine. You wouldn't end up with the typical FPS which tend to use BSP and special occlusion to do what they do in those games, but the player would know no difference provided your controller and view models were familiar or "proper" to them.
3: It is planned to support in-overworld interiors (like GTA IV, not like ENEX/GTASA), but as far as interacting from the outside into the inside and inside to the outside (I suppose like the first mafia 2 mission with the mini-gun?), I can't be sure what that would take, and it would be worth looking into, and awaiting Spark's input on whether we will shoot for providing anything like that in the core game and engine offering.
I will notify him you posted