Short answers, pulled from the story.
Lift is the component of the total aerodynamic force that acts perpendicular to the flow direction. This force keeps aircraft aloft and can act in any direction perpendicular to the flow whether in air or water.
The Wright brothers 1902 glider pulled upward with a force so powerful it defied the common intuition of the era. This upward pull demonstrated that lift is a real force acting perpendicular to the oncoming flow direction.
The equal transit time theory is fundamentally incorrect because there is no physical principle that requires air particles to arrive at the trailing edge at the same time. Experimental results confirm that particles moving over the top arrive at the trailing edge long before particles moving under the airfoil.
An airfoil reaches its maximum lift at a specific angle of attack and then stalls when the angle increases beyond this critical point. At angles of attack above the stall lift is significantly reduced though it does not drop to zero.
The Kutta-Joukowski theorem relates the lift per unit width of span of a two-dimensional airfoil to the circulation component of the flow. This theorem provides a mathematical framework for understanding lift and resolving the indeterminacy of potential-flow solutions.