Looks like Jwenting pretty much covered the first question
All structures will deform to a certain degree under loading. In the case of buildings, bridges and such structures, the deformations are more subtle and you won't notice them with the naked eye. In the case of an airplane wing, the deformation is large enough for you to be able to see it. If you wanted a stiffer wing you could make one, and you wouldn't lose any lift doing so, but you'd have a needlessly heavier wing, your ride would be bumpier in turbulence, and you would also run into the problems Jwenting mentioned earlier.
If you were to extend the chord (the width of the wing) and reduce your wingspan, you'd get a very inefficient wing, as a lot more air from the bottom of the wing would be able to spill over the wingtip to the top. This causes loss of lift near the tips (and don't have a wide wing anymore to begin with!) and you also get an increase in drag, which means you burn more fuel!
I hope this helped!