Move generation is verified with perft, the standard correctness test in computer chess: the program counts every legal sequence of moves to a fixed depth and the total has to match a number that many independent engines agree on. Six positions are tested, together covering castling, en passant, promotion, pinned pieces and discovered check, for a total of 11,024,485 positions. A single wrong rule anywhere makes the count disagree, so this is a pass/fail fact rather than an opinion.

Click or tap a piece and its legal moves appear on the board, then click the square you want. Dots mark quiet moves and rings mark captures, so the two are different shapes and not just different colours. There is no dragging — on a phone a dragged piece sits under your finger, which hides the square you are aiming at.

Level 1 if you are learning: it looks one move ahead and then deliberately chooses among moves near its best, so it makes ordinary beginner mistakes and leaves pieces hanging. Level 2 is a tidy casual opponent. Levels 3 and 4 search deeper and add a quiescence search, which means they stop giving pieces away in trades — that is usually the point where you have to start planning instead of reacting.

Yes, all three, including the fiddly parts: you cannot castle out of, through or into check, en passant is only legal on the move immediately after the double pawn push, and promotion asks you which piece you want rather than assuming a queen. Those are exactly the rules the perft test is there to confirm, because they are the ones engines most often get subtly wrong.

Yes. The Take back button rewinds to your turn, so a misclick does not end the game. Every move is also listed under the board in standard chess notation as it is played, with proper disambiguation when two pieces of the same type can reach the same square, so you can read back what happened.

By stalemate, when the side to move has no legal move but is not in check; by the fifty-move rule, when fifty moves pass with no capture and no pawn move; by threefold repetition, when the same position appears three times; and by insufficient material, when neither side has enough left to force mate — king against king, or king and a single bishop or knight, or two bishops on the same colour squares.