You'll probably get a more technical response, but since you said you need "urgent" help, I thought I'd chime in.
I have a few problems with a couple of your answers, mostly your choice of words.
First of all, I've never heard of "pressure drag". There's "Parasite Drag" (form and skin friction) and "Induced Drag" (rearward component of lift).
It could be argued that winglets reduce induced drag as they effectively move the vortex off the wingtip allowing the wing to be more efficient (again, waiting for a more technical answer, I'm not an engineer).
So, the "performance benefit" is actually *lower fuel consumption*.
I do appreciate your answer regarding the additional benefits towards stability. That wouldn't have entered my mind.
But finally, your last comment about
"air which is bleeding off the wingtip could be used by a winglet to create extra lift and therefore increase efficiency" is just pretty vague and BEGS for more technical language.
Air is never described as "bleeding" off the wingtip. Nobody would understand what that means.
There is a pressure differential that causes a vortex. Imagine a wing of infinite length (i.e., no wingtip exists). There would never be a vortex to interfere with this "perfect" wing. But in the real world we need wingtips and therefore the vortex is an accepted fact. The designers try to mitigate its deleterious effects by using the winglet to move it off the main lift producing surface so that the wing is more efficient.
In other words, the winglet doesn't *contribute* to overall lift (not in a vertical direction anyway, for the most part), but attempts to mitigate the inefficiency of our real world, less than perfect, limited (finite) wing.
The best analogy is a sailboat believe it or not, where the "foil" (winglet, sail) produces a FORWARD "lift" vector to help PULL the "ship" (aircraft) along.
Hope that helps.