Holy cow there are some huge misconceptions here.
In a most basic sense, lift can be explained through Newton's laws. The flow is "pushed down" do the plane must be "pushed up". Of course in this sense, it doesn't matter how this downwash is generated or how efficiently, only that it is generated.
Bernoulli's principle is one way to calculate the lift on a wing in certain situations (the wing cannot be separated, for example). Given a velocity distribution over a wing, you can use Bernoulli's equation to deduce the pressures on the wing and hence the lift. It says nothing about how you find sai velocities or the best shape of a wing. Bernoulli's equation is merely a tool; it cannot explain lift completely.
Now, any wing that generates lift must, by definition, deflect the air downward, and the same wing will also have a higher pressure below than above. You can connect the two using what is called the Kutta condition. This states that for an object with a sharp trailing edge, the rear stagnation point must be at that trailing edge rather than the location predicted by inviscid methods, which results in a net circulation around the airfoil and therefore a velocity difference and pressure difference on the surfaces as well as deflected flow coming off the back. This works for any shape with a sharp trailing edge (as all wings have) and does not require any assumptions about how the plane is flying.
A plane with a symmetric airfoil can fly because it has angle I attack and a sharp trailing edge. This allows the airfoil to deflect the flow downward. The same applies for a traditional airfoil flying upside down. In this case, flying inverted is her inefficient, but with enough angle of attack it can be done.
Flying vertically doesn't have lift in the traditional sense. The lift is provided solely by the thrust.