The situation is more complex than what statistics is telling you. A chess has a fractal structure, that is given, and this is actually explaining the high number of positions. Some endings are quite obviously fractal, because the outcome depends on, even though the arrangement is the same, whether the position is to the left or to the right of the center and so on.
White wins 37.35%
Black wins 27.41%
This is actually answering the question if black wins more often than white. But that is not the question. Draw is a position when neither white nor black can win, but this is really far from white and black being equal. Only if we would analyze draw positions and measure the positions value, we could really add something to this analysis. What I'm saying is that this analysis has to be refined. At least it would have to be done separately over all possible combinations over the first move (2 plies), since black and white have a predefined set of choices. They simply have to move some of these.
Once this is done, you would eliminate those that are giving a strict advantage to the white or black.
Additional analysis would have to say the percentage of games where one player played a blunder. This would eliminate most of the psychological elements of the statistics.
Now you are left with how humans, and this is very important to understand, humans play chess. With the advent of computer chess, you can find that almost all chess players call the moves a computer makes: a surgical and sterile, something that is mathematical correct, but generally devoid of any strict plan or idea.
And here comes the problem:
Can you describe every move in chess by human logic in form of attack, tactics, defense, trap...? The answer is a resounding no, and this is why a computer can play "better", because it is not human. It knows about the logic of how human plays since its algorithm contains it, but it does not understand the game the way a human does. It constantly measures.
Since how humans play is not mathematically the most precise way of playing, here comes the question of our knowledge about chess, i.e. what part of chess can we describe and learn?
So if you take that the answer to 2 is very much but not sufficient, since it seems that computer will be able to reach 3500 or maybe even 4000 ELO quite soon, while humans will not go much beyond 3000 ELO any time soon, we probably can play, at best, at about 80% of how chess can be played in order to decide if chess is draw.
Regarding the way humans play chess, it seems that white might have a decisive advantage because the theory around how black should play in order to win is not developed enough. Since chess is a fractal game, any mistake black makes is then easily more detrimental to the final result than a similar error white would make.
Basically a small disadvantage a black has, because of the initial position AND knowledge we have, is putting him instantly at the edge of the known human logic of playing chess. A player must be more cautious and more inventive and any small mistake white would make requires more effort to turn into a full advantage.
Theory of chess grows, but the total effort of a relatively limited number of players will always be limited by human intelligence. At the moment, if you look at the statistics, you can see that the best lose a little bit more between black and white, Carlsen 10%, the rest about 60-80%. But none of them know how to win with black. In that sense, it is obvious that our current knowledge gives the white a sufficient advantage to get a draw easier. And this is placing black in a disadvantageous position not to make a mistake. And then word "human" comes into play.
Once computer reaches 4000 ELO we will know much better if chess is really a fair game. Until then white has a sufficient advantage to place black into a submissive position. It would be great to calculate this in form of ELO points, of course. I cannot know but I think it is less than 100. Regardless of this random guess, it is a definite conclusion that we have to speak about how we play chess and how chess can be played as two very different topics.