The board is a grid of lights, some lit and some dark, and it is solved when every light is off. Clicking a light flips it and the four lights directly above, below, left and right of it, so each click changes up to five cells. Edge and corner clicks flip fewer, because the missing neighbours do not exist.
The only number is Moves, and lower is better. Every click counts, including one that undoes an earlier click. When the last light goes out the message confirms the solve, and if the count beat your previous record for that size, Best is updated. Best is kept separately for 5x5, 6x6 and 7x7, shows a dash until you have solved that size, and is lost when you reload.
Yes. Each board is built by applying random legal presses to an all-off grid, so reversing them always works.
No. Each size keeps its own record, and all of them reset when you reload the page.
Yes. On a touch screen the game shows on-screen buttons, and games played with a mouse work by tapping.