My responses are in blue.
2.The suspension is absorbing some of this pressure, we know this because the right tire is lifting up.
Absorbing?
Yes, absorbing. If the tire "lifts" while the chassis leans that means that there was extra downward pressure that is no longer going to push down on that tire because the spring absorbed the energy. A stiffer spring, swaybar, or suspension (roll center) is changing where the force goes.
3. Not all of the weight that has transferred is being directly applied to the tire.
Clarification for what you mean exactly by "not ... directly applied to the tire"?
The pressure that would have been applied if we had no suspension (assuming a perfectly flat surface) would have been higher than the amount of pressure pushing down on the tire after you factor in the energy that was absorbed by the spring, swaybar, and suspension.
4. With a surface that has ample traction (lets say for a moment that it is ideal and there is no slide) there is no need for the right tire to lift, in fact if it pushed down it would actually help us get MORE traction.
Yes and no. Yes because the higher traction surface you are on, the less need for weight transfer (or lift as you called it) and this is exactly why stiffer springs or swaybars are used on on high traction surfaces. If there is no need to generate more traction, you want to minimize losses due to chassis sway and the like. No, because with the chassis leaning over there is literally more weight on the right side. Since the sum of the forces must equal zero in a constant state system (which this is for a sitting chassis that is leaning over) there is more pressure being placed on the tire since there is more weight on it. There is no lost force. You are thinking of a state of acceleration when you say if it 'pushed down' it will generate more force. If the spring pushes down harder than there is weight on the chassis, the chassis accelerates upwards. In that instant you will have more traction, but as soon as you stop the chassis from accelerating up it is gone.
On the higher traction surface you naturally have more weight transfer than on the looser surface assuming that the vehicle weight and speed is the same. See this is where it gets confusing. Assuming that two of the exact same car/truck took the same corner at the same speed and everything was the same except for the suspension (one stiffer one softer) there would be the same amount of weight transferred assuming that neither lost traction. The inertia is being redirected from straight ahead to towards the left, but from what we know about inertia it does not want to move. Since the center of gravity is higher than the surface we are turning on the weight of the chassis is rolling to the right. Now here is the majic, the car/truck with the stiffer suspension is resisting the roll much more than the other car so more downward force is being applied to the outside tire and less to the inside tire than the car/truck with the softer suspension. Just because one car leans over more does not mean that it is transferring more weight. Focus on where the weight is going rather than how much is transfering. With a soft suspension it is constantly more even across the left/right sides of the chassis than with a stiffer suspension.
If you want to see this concept in action watch a fast drag car launch. Your initial thought would be that the best launch would transfer a bunch of weight to the rear, the suspension would squat, and the car would launch and be gone. In reality, most fast drag cars do not squat at all they actually stay rather level or the rear of the car lifts (anti-squat) getting the maximum amount of force to transfer from the chassis directly to the tires and then into the ground.
They don't squat because they don't need more traction. They are trying to resist blowing over backwards. If you don't need more friction at the tires you want to minimize those losses. Let's look at another drag racer; the snowmobile. We drag race them on all types of surfaces... asphalt, grass, snow, and even water. Comparing the asphalt drag snowmobile that has literally unlimited traction to a snowmobile on grass or snow that don't have unlimited traction you will see two completely different results at launch. The asphalt sled acts just like a dragster. The snow/grass racer squats so much the front skis are hovering over the ground as all the weight transfers to the rear to maximize the available friction.
They do need traction, on a perfect flat surface with tons of grip you get the most traction by maximizing how stiff the suspension can be. This may not translate as well because it is a polar opposite to our situation but I know this is true.
Of course it is different in our application because we are A. Talking about turning and B. on a sub optimal surface. The challenge becomes figuring out if the suspension reaction is too stiff causing too much weight to be applied or too soft absorbing more of the weight that should have been transferred. In all reality (not quite sure but it should be right) the same amount of weight is transferring from left to right its just where it gets absorbed or transferred that we are trying to control.
Again, too soft doesn't 'absorb' anything. The force gets to the ground no matter what.
Are you sitting at a desk? Good...Grab a pencil and grab a rubber band. Take the pencil and put it down on the desk so that the end is hanging over enough for you to grab it, make sure the rubber eraser is away from you. Now grab the end, transfer weight from your side to the end (lift it up a little and push down) and try to push it away from you. Now grab the rubber band and do the same exact thing. What one transferred more weight into the "tire"? Your rubber band (spring) is absorbing the energy and storing it for later, when the weight is lifted it goes back straight. Now I think one of the important functions of the suspension is to "dampen" the shock of the weight transfer so that it comes on evenly otherwise there would be too much energy too fast and you would loose grip very quickly. Its all about balance, the weight of the truck is always pushing on the ground its just a matter of where it is pushing. Remember this test was of two polar extremes.
I think I confused you because I was only talking about one tire in my initial response, its more of a right vs. left who gets the force rather than it magically disappearing. In place of the pencil vs. rubber band experiment you could do a similar test with an onroad car vs. offroad car. Put them on scale, roll them over and see what the scales tell you. You could of course try it on your truck and just swap springs between the softest and hardest you have to make sure chassis setup isnt playing a roll.