Those symbol represent faction items. Right now, it doesn’t do anything, but it will be part of faction and uniform / disguise system.
As for the bear ruin door, that’s an entrace to the endgame dungeon. You can enter it once you finish the main story quest that is partialy in the game.
If you want help, you can read the spoiler below.
Spoiler
Enter the beach with the cave anytime after about 10 weeks pass since the start of the game. You have to be alone without any companions. You will see a cutscene with a ghoul. That’s how you know you are at right spot.
Next, wait untill about 16 weeks pass since the start of the game and enter the forest area with the bear. Alone with no companions. Again, you will see a cutscene.
Continue playing normaly. After a few more weeks, a cutscene will trigger at the start of a week automaticaly.
After that, you will get another cutscene few weeks later, at the start of the week, automaticaly.
This will give you a new quest. Raise your stats, get some equipment and return to the spot where the last cutscene took place. You will enter a new dungeon. Finish it and you will get a key that will let you open the bear ruin door.