How are the scores decided in Chess? Consider the following pictures:





I would like to understand the following:


My understanding is that it depends on the opponent's move against our move. Am I right?
What is the minimum and maximum range of the score?
When one can achieve the maximum score at very first move?
What is the use of the score?


(Sorry for asking very basic questions. Newbie for the Chess stuff).
Those aren't scores; there are just three possible scores in chess: White wins, Black wins, and draw.

Those are evaluations of the chess engine; a score of +0.62 means the engine thinks White's position is better by 0.62 pawns. A negative score would mean Black is better. On professional level, a score of 1.5 pawns is in most positions decisive, i.e. enough to win the game. However, weak moves by the players will change the evaluation.

The maximum and minimum score depends on the chess engine you're using. If you play the game till checkmate, you will see that the scores will get larger (either more positive or more negative) until you see something like +#8 which means White can mate in 8 moves.