I will start off by saying that my conclusion will most likely not be sufficient with more users adding their data. Consider the following graph as my data point: This graph was taken on March 19, 2016, at 11AM. The spread of race and profession seems to indicate that there is a relatively even distribution of professions for each race. However, there are some interesting points to consider. Consider Hypothesis 1 regarding Sylvari Ranger. This can be seen in the graph as true, since the Ranger node is closer to the Sylvari node than any other race node. Asura Engineers, from hypothesis 2, falls short, since there are even number of Asura and Charr Engineers. Hypothesis 3 also falls short, since the only profession closest to Charr and Norn is Guardian, which is also equidistant from Human. Hypothesis 4 is also incorrect, since there are more Human Thieves and Human Revenants than other professions. Again, this is a very small sample set of data, so these results may not represent the entire population fairly.
In conclusion, there seems to be very little connecting races and professions. Players will choose to make all of the possible race-profession combinations, with little connecting one race to one profession. I believe that this indicates that games should always include the option for choosing race and profession when such options are available. From this data set, I would declare that there is no innate connection between races and professions in Guild Wars 2.