How to see what applications do some actions when I power on my phone? I believe there's some set of “hooks”, which get executed when I power on the phone. I want to see it to figure out the reason why my phone sometimes doesn't wake up properly (wakes with black screen).
While the logcat option recommended by Ryan of course is a valid possibility, it is not the most user-friendly solution. I've got a better idea :)

Apps started automatically after boot registered for a certain event, called BOOT_COMPLETED. To do so, they need to request this permission (you find it under "more" on the playstore pages) called "Start after Boot" (or, with its technical name, BOOT_COMPLETED -- what a surprise!). So to figure out which apps could potentially be in here, you can use a permission checker. There are many of them in the Playstore, but I will mention only two of them to get you started:


PermissionDog1
RL Permissions2


 

Both let you browse your apps by permissions, and even try to indicate "potentially dangerous apps" -- nice side-effect in your case ;)