As I understand, the work is force times distance, but force in the equation isn't really (vector) sum of all external forces acting on the object in question, but only (again, vector) sum of all active forces acting on the object. As you probably know, for every action there is an opposite reaction (3rd Newton law), thus if act on an object with an active force, the reaction force formes in the opposite direction.
So basically, if you push an aircraft with force 1 kN for 100 meters, the work done is 100 kJ, even if the forces acting on the aircraft are in equilibrium (the resultant of all external forces acting on the aircraft is zero) and the aircraft is consequently moving at a constant speed.
As for the first question, it is very simple (or very complicated, but I'd rather use the simple explanation). To gain lift (or aerodynamic reaction, whatever you call it), you need difference between pressure on the top and on the bottom of the wing (Bernoulli's theorem) and usually this is created by exposing a wing profile to an airflow. In order to create an airflow, you have two choices: either fix the aircraft and move the air with a fan (for ex. wind tunnel), either move the aircraft through a still air (which is what we want to do, since aircraft are a means of travel). So if we want to move the aircraft through still air in order to create an airflow, we must create a force, which moves the aircraft in the desired direction (let's say forward) and that force is called thrust. And to create thrust force, we need to convert fuel into rotating force and create thrust either with turbojet engine either with a propeller (you could do a PhD in thermodynamics, but for the sake of argument it's really not worth going into details how fuel is burned).
So to summarize it: converting (burning) fuel creates thrust force, which moves aircraft through still air, therefor creating airflow to which wing is exposed, hence lift force (and drag of course) is created, and the aircraft flies.