4. This doesn't seem counter-intuitive, as more lift on the front end will tend to make the car understeer, and that's the more inherently stable tendency.
5. I'm sure I read in a book somewhere that lift or drag translates directly to work. If the airflow is doing work it will show up as force on the car. So as calz says, if you clean up the airflow under the car so that it isn't turbulent, you can reduce drag and lift, as it has to do less work to get under the car - acting less like a parachute. If you have a lot of lift, that's a sign the the air is doing more work. Closing the huge hole in the front and ducting to the radiator prevents all that air from packing into the front and pushing up on the hood. This will reduce lift and drag. A spoiler on a Z reduces lift and drag as well (to a point, after which it will reduce lift and increase drag).
7. The further away from the axle the more leverage you have too. So a rear wing can be mounted lower and further back and make more downforce than the same wing mounted in cleaner air and higher in some circumstances.
Thinking back to what might be the same video about splitters, I think his view on the shape of a proper splitter is a little simplistic. Most of the time on a race car you're rule limited, or you have practical constraints that limit the shape, but in the more unlimited classes you see the upturned nose of a splitter or a raised tunnel entrance in the front. There are also interesting front wings on open wheel cars that we can learn a little bit from where they have unusual profiles: relatively high in front, flat and close to the ground for a bit, then sloping up at the back. Not unlike McBeath's drawings of what an undertray should look like, but with a more wing-y looking top side.
Most low level race cars use flat splitters, but diffuser on the splitter kind of aim for the same sort of shape in the back as the wing. If you're going to design a splitter I'd suggest a close look at what AJ Hartman is doing. He's working with high level aerodynamicists, does lots of CFD and wind tunnel testing, and makes good stuff. Then he makes youtube videos telling you how to DIY it. Pretty amazing, really. Note the front lip shape. Sharp on top, rounded on bottom.