1, 2, 3: short answer no. Long answer yes.
To be blunt: yes it's technically possible but it's not going to happen. There hasn't been ANY games made in CC that have done this. While there are network implementations in both Python (PodSixNet) and other libraries, none of which I've followed lately, extensive networking capabilities aren't there.
Your third question about lag is closely related to what I said: I recall that even one of the more popular and complete network plugins didn't have interpolation (which is essentially data prediction to contravene the inevitable effects of lag). There haven't been any P2P networking plugin releases that I'd know of so you'd have to utilize traditional sockets anyway.
All in all networking is something that is more often than not immediately out of question for developers with diminishingly little experience.
4: Sure, look at the behaviors you can add to objects. Construct isn't a package that supports only certain kind of gameplay similar to, say, RPG maker.
5: Yeah. You'll just have to have a system that remembers a few numbers that you'll be able to use as positions. It's almost laughably easy once you grasp the concept.
5b: Can be done instantly with built in features. Just have a sprite with Mouse-behavior and tick Center view on me -attribute. It'll need some tweaking though, because the mouse coordinates will change every tick (the game progresses with ticks that for the sake of convenience can be perceived as frames, although they're not one and the same) and the movement will be very quick.
If you want to scroll when the mouse touches the edges you'll have to compare the mouse coordinates (mousex,mousey), or whatever you use as a cursor, and move the screen accordingly once the cursor is close enough to a viewport edge.
6: Definitely. There's a built in behavior for Line of sight that can be utilized. If you mean literal fog of war type of darkness, sure, it's easy too. For example you could have a non-transparent pitch black layer with the Multiply-shader. Once you add white objects (similar to built in object Light) to it it'll show through. There's so many ways to do this.
7: Of course you could. "Anything" is possible gameplaywise. Think of it as a tool, not a mold.
8: Yeah, in fact it's a built in feature.
Edit: Disregarding the first three points it doesn't really make a difference whether you want to work with Construct Classic or Construct 2. CC is in its own right more mature and has plenty of 3rd party plugins around. CC also has stackable HLSL shaders, which elevate its graphical capabilities beyond outstanding. C2 on the other hand has had a much more structured approach on its development and is quickly approaching CC's level in both performance and features. C2 however isn't there just yet. C2 does have much more support though, CC is essentially a community supported piece of software nowadays.
CC is open source and isn't restricted like the free version of C2 is so you might find it more comfortable to learn game development with. Either way knowledge on CC translates to C2 and other way round in case you want to make a switch at some point.