This depends on the piece you're moving, as you can move a knight as an opening move, but the knight's awkward L-shaped pattern doesn't usually translate to a number of spaces, per se. You're probably thinking of the pawn's initial move, as the pawn is the most commonly moved piece for an opening move.
The pawn can only move 1 or 2 squares from its initial position, and then only 1 square at a time after that.
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A total of three. The knight is the only piece that can change direction in a move, but can only move three spaces. It can move one space forward or back, and two spaces left or right, or it can move two spaces forward or back, and one space left or right.
Yes, when in the center of the board a knight can move to a total of eight squares.
If you still are not sure i highly suggest reading a Chess book.
A castle, or rook, can move in a straight line as far as possible as long as it doesn't run into other pieces. It cannot jump over pieces.
As many as it can (legally) along the same unimpeded diagonal. The maximum would be 7, as the longest diagonal available is 8 squares.