If there was perfect play from both the colors, will white win because of the first move advantage or will it be a draw?
Most Grandmasters will argue that chess is a draw with perfect play from both sides. However, in practice it is shown that white has higher win rates than black, but this is due to the first-move advantage. This is because white technically gains a small advantage from having the first move, and black will equalize with their move.
It is possible that a first-move could cause a disadvantage with perfect play, because despite having perfect information, the black player could potentially be able to counter any strategy white attempts to play. It is more likely however that if one side were to have a forced win, it would be for white.
The answer to this question will not be known for a long time because only in 2012 were endgame tablebases able to solve any position with 7 pieces perfectly (including the 2 kings). For comparison of how impressive this feat is, 6 pieces was only solved in 2005. Obviously, this problem is exponential because with more and more pieces, the complexity increases further and further, until eventually the game is solved for 32 pieces. One could argue that the starting position is static so we don't have to consider every combination of 32 pieces on the 64 squares, but the number of possibilities is still enormous and will take a long time to know for certain.
Almost all experts during the last 150 years share the opinion that the game should be a draw with perfect play (link):
The view that a game of chess should end in a draw given best play prevails.
We have not mathematically solved perfect play in chess yet. However, chess computers represent our best understanding of nearly perfect play, and about equal strength engines overwhelmingly make draws from the starting position. Usually the only way to get a decisive game is to force computers to start from a risky or unbalanced opening, so computer tournament organizers use opening books to test interesting positions.
It is the Zermelo's theorem from game theory, which says that a finite 2 person game always has a solution (draw or a winning strategy for black or white).