- The real answer is so hard to compute that there is a million dollar prize attached to it.
- Today, we design planes using approximations and trial-and-error. It works well because we are very experienced in designing planes, sometimes at the cost of many lives, but it is not exactly a "first principles" approach.
I think what people usually mean when they say that we don't understand flight is that there are no simple equations. A lot of physical problems have elegant solutions (eg. the shape of a hanging chain is roughly the cosh function). But there are no elegant equations that describe the profile of a wing, so it's a bit unsatisfying.
You can have lift with laminar flow. In fact, the article includes an explanation of the usage of the Reynolds number to characterize laminar and turbulent flow and how the flow around plane wings is clearly laminar (called "smooth" in the article).