1. Possible with Lua using object / animation position, object rotation field & mouse position.
2. Special regions? In regards to characters walking, running, crouching, jumping, swimming etc, that is what character outfits are for. Character movement & actions are essentially animations, even in engines like Game Maker Studio, it is the animations that provide the suggestion of what is happening on screen to the person playing the game. Sure gravity & movement also come into that, but you get the general idea.
3. Simple battle? Questionable, but probably possible with action parts, animations & maybe with a bit of Lua script - may even be possible without scripting, but who knows.
4. VS is not designed for non-adventure (point & click games) because it is a specialist engine designed exactly for point & click adventure games, but sure, in theory, it is possible to use it for other genres, but there are engines more suited to other genres, than trying to use VS to make them.
5. Can AGS really do that? It's not exactly hard to achieve that in VS either. Just create another object with the image / animation inversed. If it's a water reflection then you could even apply one of the shader ripple effects to the object containing the reflection. A true mirror effect on the other hand, where it displays your character in them, would probably be possible with a bit of work, but I assume that that would require a bit of work in any engine.
6. Possible with either the in-editor key actions & conditions or with the Lua keyboard event handler; even though the engine isn't designed for keyboard control of players, it is still possible, but would require work to correctly calculate movement angles.
7. That's what the way system section of the editor is for. You can define the places that the character can walk by defining borders & paths. You can create multiple way systems for each scene & swap them out as needed.
The only thing I am going to say is this: Personally I don't care whether or not you decide to use Visionaire Studio, or another engine. It's entirely up to you & what you feel comfortable making your game with. Visionaire Studio is exactly what it is, no more, no less. All engines have their strengths & weaknesses - all are far from perfect.