As in original shogi, the captured piece transfers to the Hand and it can be returned later back to the board. Player can select to do his move on the board or to return piece from hand to any empty square on the board . The last one is called Dropping. It's illegal to check by dropping a piece. When it's Black's turn the Kaze and Arashi are Black's pieces, and when move will change to White, the same pieces are White's pieces.
Same rule relates also to pieces in hand.
Because Arashi and Kaze are shared pieces, they can also captured each others regardless of own or opponents pieces. Still the other shared piece can capture the checking piece. Although Black's Arashi reaches to threaten White's King, Arashi hasn't contact to Black's own King. Now White can't capture the checking Kaze with his King, because Kaze is checking piece. Checking piece makes necessary contacts with Kings regardless directions of pieces.