The score is unique for each arena, some arenas even do not have any. What happens outside the Late War Main, will stay outside the Late War Main.
You can check your score either in game by rightclicking on a name on the roster and selecting "score", or by using the .score [NAME] dot command. If you are looking up your own score, you don't have to type the [name]. On the AH website you can find a much more detailed display of score and various stats, just click on "Scores & Stats"
Read
here how scoring works
Lastly, score and perks are just distantly related to each other. Perks points are not generated via score. One can have very good score, but still earns very few perk points because he is flying a lot of 'awesome' low ENY planes. (
See here for a basic explanation how perks are generated)
But practically score doesn't really matter. in game. It serves only two purposes: Determining rank which is only used for command of CV task groups, and as a cheap 'explanation' why one player doesn't play the way like another player is expecting him to do
And a final word of Gastropodic Wisdom: There is no risk in totally ignoring score (it's all about having fun after all), nor is it a bad thing to watch and to improve it (quite a number of players will try to convince you of that), but being score
fixated can have a negative impact on your ability to enjoy the game.
