Thank you for your comment!
The character doesn't suddenly die, it all depends on their courage meter. Some characters get spooked by ghosts even if they are far away, while others have to be too close to a ghost to die. In compromise, some characters can jump higher / run faster.
Should have clarified that more in the game, my bad :)
I am also aware of the jumping issue. I left this bug for last, but never really tackled it due to lack of time.
Glad you enjoyed it (to some extent, at least).