just checked: bosses 100%,items 76%, exploration 97%. so I am still missing stuff. still no idea how to get past the laser barriers.
The lasers you mentioned should be deactivated after the death of the 4th boss.
That door in the main menu is just a decoration. It's there to show that the player enters the mountain.
For the interactable map, it marks items that are still uncollected. After using it, you can open the map in the menu then hold ctrl and scroll the map with wasd (keyboard), or triangle and directional keys (controller) to see uncollected items denoted by question marks.