I was wondering about the salary increase you get with every new level. I know that the salary is representative of my score for that level, but do you actually receive that amount of money at the next level or at the end of the year of the next level?
I'm just wondering if there's any point in continuing running a hospital, even after reaching the level criteria, in order to try and increase my salary.

You don't receive that money, it's just a fancy way of saying "You've finished this level with that score, are you ready to move to the next level or do you want to play one more year before you go?". Really the only reason to keep playing is if you like the current level and want to improve it some more, for the sake of completion or because there's one thing you didn't finish and OCD compels you to fix that before jumping to the next level.