1. If i do entity.setHealth() will the EntityDamageEvent trigger? 2. What happens if you cancel the PlayerJoinEvent/PlayerLoginEvent?
No, it shouldn't. I'm working on a custom health system at the moment and I have not had any damage events triggered for changing the health value. The player will be kicked. I think you have to specify a message though for it to take effect. Atleast in BungeeCord.
If you took the time to read the Javadocs, you'd see that the PlayerQuitEvent does not implement Cancellable.
Yeah I never really stop to learn the methods and stuff, my bad EDIT: Wait I said PlayerJoinEvent not PlayerQuitEvent