Convert OMI NO2 Vertical Column Density (molecules/cm^2) into Mixing Ratio (ppm)
No, you shouldn't really do that.  A vertical column density (VCD) retrieval provides the user with a representation of the total number of molecules over some vertical slice (e.g. the entire troposphere).  A mixing ratio, often defined in parts per million, is meant to express the average number of molecules in a parcel of air.  The problem with converting VCD to ppm is that the troposphere is a whole lot more than "a parcel of air".  The density of air and mixing ratio of NO2 changes as you move vertically through the atmosphere. So, saying that NO2 has any one mixing ratio through the troposphere is really not appropriate.  

There are methods you could use to estimate ppm NO2 from VCD (such as inferring mixing ratio from the shape of the a priori profile), but they would be inherently uncertain for many reasons:


The retrieval of tropospheric NO2 from OMI is not representative of the surface, but rather a well-mixed free troposphere.  
The NO2 product is dependent on a global model to subtract the stratospheric contribution.  
There are many quality control steps needed for quality assurance, such as accounting for clouds, terrain, surface albedo, detector issues (e.g. striping or row anomalies), etc. 


In my experience with OMI tropospheric NO2 data, any expected temporal correlation to daily surface measurements is futile.  You will sometimes find temporal correlation at the seasonal or coarser scale, for what that is worth. 

Spatial correlation with models and surface monitor networks should be expected, but your results will be highly dependent on your 3D spatial comparison methodology. When comparing to a model, you will want to apply the "averaging kernels" which help to remove the dependence on the a priori profile of the satellite retrieval.  

In general, OMI tropospheric NO2 data is useful for identifying large emissions sources that are missing from air quality models.   It is also useful for identifying inconsistencies across political borders that appear in air quality models due to old emission inventories (e.g. mixing circa 2006 Canadian emissions with circa 2011 USA emissions).