1) No real way, but if you draw a construction line, half of your profile, then mirror it....it'll be symmetric.
2) Just what it says. The extrusion will be equal distance from the end face to the plane they're extruded from. It doesn't need to be symmetric.
As far as your first question I think your asking if how can you tell if a sketch entity is declared as symmetric?
If you see the glasses in the top center of the screen and toggle on the "View Sketch Relations" or you can also do this from the view menu. You'll see all sketch relations as well as the dimensions. The symmetric constraint looks like a box with a slash through the center.
The mid plane creates an equal amount of material on either side of the sketch plane (by default). The sketch plane is defined when you first create the sketch. You can choose another plane to make as the mid plane by changing the "from" drop-down in the extrude command.
1. For a sketch to be symmetrical it needs to be the same on both sides of the center line, wherever you decide to place the center line. If you can place a line in the center and the sketch segments are the same on both sides of the line it is symmetrical. You can make it symmetrical with your design intent and then if the part needs a little something different on one side or the other you can add that as an additional feature if you desire.
2. extruding "mid Plane" is just that. If your part is 6" it will extrude 3" each direction from the sketch plane. Again you can then create cuts or other features based on one side or the other of the sketch plane if you need something that is not symmetrical.