Zero theory heavy question/puzzles

1. I assume you know how chess pieces move and how a game can end for this one:
   Assuming a format of double chess, where both players can move twices (either 2 pieces or same piece twice in a move), which side would you prefer to play with (assuming there's money on the line)?
2. If you rolled a fair dice infinitely many times, whats the average value of the numbers u will get? (Hint: =/= 3)
3. How can u go south one unit, go left one unit, go north one unit and be where u started?
4. Is it better to go along one side of a rectangular path or go along a hypotenuse? (and why? prove <3)