It really varies. Some manga have characters who can keep secrets well, while in others, secrets are spilled easily. It all depends on the story's context and the personalities of the characters.
I'm not sure. It depends on the specific manga you're referring to. There could be various plot developments and character relationships that determine who it is.
To keep a secret, I first try to forget about it myself. I don't let it linger in my mind too much so that I'm not tempted to share it. Also, I avoid situations where the secret might accidentally slip out, like when I'm drunk or really angry.
Perhaps the secret is that Lucy has a unique magical item that is very powerful and dangerous. Natsu keeps it a secret because he doesn't want other mages in Fairy Tail to get greedy or misuse it. This item could be something that was passed down in Lucy's family and she doesn't fully understand its potential yet.