Turbulence isn't the same as unsteadiness - a vortex street is not necessarily a turbulent phenomenon. As an analogy that (for some reason) I find easier to understand, consider a convection experiment where we heat a fluid at the bottom and cool it at the top. Below a certain threshold value for the temperature difference, the heat is transferred only by diffusion and there is no bulk flow. A little higher and we get an instability, resulting in the formation of a convection cell. In this case the fluid is moving, but it is still moving in a laminar way. As we increase the temperature difference, the speed of the flow increases, and it's only when we've increased the temperature quite a bit more that the flow becomes turbulent.
Vortex streets are similar. Above a certain value of the Reynolds number, the vortex street forms. The flow is now time-dependent, but it's periodic and still relatively easy to predict. If the flow is increased even further then the vortices spin so fast that smaller vortices form to dissipate their kinetic energy. It's only at this point that the flow becomes unpredictable and chaotic, which is when we call it turbulent. I guess you can say something like, a Kármán vortex street is a flow that's unsteady on one spatial scale, but in order for a flow to be called turbulent it has to be unsteady across a wide range of scales.
This is a very good question! Drag due to viscous effects can be broken down into 2 components:
$$D = D_f + D_p$$
where $D$ is the total drag due to viscous effects, $D_f$ is the drag due to skin friction, and $D_p$ is the drag due to separation (pressure drag).
The equation above demonstrates one of the classic compromises of aerodynamics. As you mention, laminar boundary layers reduce the skin friction drag but are more prone to flow separation. Turbulent boundary layers have higher skin friction but resist flow separation.
$$D \quad\quad\quad=\quad\quad\quad D_f \quad \quad\quad+ \quad\quad \quad D_p\quad\quad\quad\quad\quad$$
$$\quad\quad\text{less for laminar}\quad\quad\text{more for laminar}$$
$$\quad\quad\text{more for turbulent}\quad\quad\text{less for turbulent}$$
Generally speaking the more "blunt" the body is (such as a golf ball) the more likely adding dimples to trip the boundary layer will reduce drag. Airplane wings are less prone to separation since they aren't as "blunt" and as a result skin-friction drag is more important.
For more information see Section 4.21 of Introduction to Flight by John D. Anderson
EDIT:
Laminar and turbulent boundary layers are fundamentally different in many ways but the important aspect for flow separation is how "full" the profile is. The figure below is a schematic comparing the mean velocity profile of a turbulent boundary layer to that of a laminar one. $V$ is the velocity tangent to the surface and $\eta$ is the distance away from the surface. As you can see, for turbulent boundary layers, the fluid close to the wall is moving faster than for the laminar profile.
![Schematic of laminar and turbulent boundary layers.](https://i.stack.imgur.com/HRCxR.jpg)
What causes the flow to separate is an adverse pressure gradient, or $dp/dx < 0$ where $x$ is the coordinate along the surface. Generally fluid moves from high to low pressure. In the case of a boundary layer that is on the verge of separating, the flow is locally going from low to high pressure. The figure below illustrates the effect this has on the boundary layer. When the flow near the wall begins to reverse, the flow is beginning to separate. Because the fluid in a turbulent boundary layer near the surface is moving faster, a turbulent boundary layer is better able to resist an adverse pressure gradient than a laminar boundary layer.
![Effect of adverse pressure gradient on a boundary layer.](https://i.stack.imgur.com/SuMe2.jpg)
Most objects that are designed with aerodynamics in mind are slender. This is done specifically to reduce the adverse pressure gradient ($dp/dx$) over the surface of the object and reduce the possibility of flow separation.
![Drag on slender vs. blunt objects.](https://i.stack.imgur.com/tpy4w.jpg)
Figures are from Fundamentals of Aerodynamics by John D. Anderson.
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Mythbusters covered this one. They found significant fuel saving at constant speed. Assuming their findings are correct I can only guess that the technique is not used for cosmetic reasons ie few people would want to drive a car that looks like it has been in multiple accidents and covered in dents