A chess clock (or game clock) gives each of two players their own countdown timer, where only one side's clock runs at a time — pressing a button stops your own clock and starts your opponent's. It's used to enforce time limits in chess and other turn-based games so that thinking time is fairly and clearly divided between both players.
Yes, you can add an increment (extra seconds added to a player's clock after each move), matching common formats like Fischer or Bronstein increments used in standard timed chess.
That side's clock stops at zero and is visually marked (e.g. highlighted in red) to indicate they've run out of time, per standard chess clock convention.
Yes, each side's starting time can be configured independently, which is useful for handicap games where one player is given less time than the other.