Here are the answers to your chess questions:
Question 13: True
In chess, a draw can happen by repetition of moves.
Question 14: False
You cannot castle when the king is in check.
Question 15: True
The objective of chess is to capture the opponent's king. (Technically, it's to checkmate the opponent's king.)
Question 16: True
Checkmate occurs when the king is in check and cannot escape.
Question 17: True
A king can never move into check.
Question 18: True
Castling can be done only when neither the king nor the rook involved has moved previously.
Question 19: True
A pawn can be promoted to any piece except a king.
Question 20: True
The chessboard is made up of 64 alternating colored squares.
Question 21: False
The rook can only move horizontally or vertically, not diagonally.
Question 22: True
The king can move one square in any direction.
Question 23: True
A knight can jump over other pieces.
Question 24: True
En passant is a special rule that applies to pawns.
Question 25: False
A bishop can only move diagonally.
Question 26: False
The queen is not the only piece that can move both diagonally and horizontally; the rook can move horizontally or vertically, while the bishop can only move diagonally.
If you have further questions or need clarification about any chess rules, feel free to ask!