In other words, after white's move, black king is not in check. It is now black's move, but any move that black could make results in check. Is this a checkmate? Is there a chess term for this situation?
- Putting your king in check is not a legal move as you've realized.
- Of course, if Black has any OTHER legal moves he can and should play one of them!
- If a side TO MOVE does not have ANY legal moves, that would be a stalemate, not a checkmate (which is delivered only by the side making the check)
It's called a stalemate, which is a draw.
No, if there are no more moves available to black then it is a stalemate.
If black has other pieces which have moves available to them they must move those pieces.