Who has winning strategy?

Question

Game board is a square -(2n + 1) <= x,y <= +(2n +1).
All nodes with integer
odd abscissa x and even ordinate y are marked red, and
even abscissa x and odd ordinate y are marked blue.

http://alexandersemenov.tripod.com/game/index.htm

The red player begins and can connect any two adjacent
red nodes with red pancil.
Next half-turn the blue player can do the same with blue
nodes.
Edges already marked cannot intersect.
The player who connects the opposite shores of his color
wins.

(a) Prove that the game cannot result in a draw.
(b) Who has winning strategy?

The picture depicts possible state for n = 4, after 4 1/2 turns.

Winning strategy is highly symmetric.

Answer 1

If they play in turns, they both can't close at the same time. So I guess a draw is not possible.

From what I see, the red player has an advantage in theory because he starts. But from the diagram, I think blue has an advantage. If he can block that vertical line, which he has started to do, then the red can't go across.

But there's obviously a lot about the game I don't understand at this point.