I play an Inquisitor, and I don't know how to open locked doors and chests. Do you have to play a thief to have some kind of lockpicking or did I miss something?
I'm stuck at several quests surely because of my inhability to unlock doors and chests !

well, there is a spell that opens locks .. shatter, i guess it destroys the lock mostly

Also you can attack the lock by standing net to it and holding shift + attack

Bash them open. Just attack them until they get destroyed - when you see chest / door losing HP, you're doing it right. And at early levels, they take forever to bash (several hundred HP), so ... Be patient.

Thanks to you both, i'm gonna try that right now!

Just the unlocking with the lock picking skill gives you experience points so I recommand this. I have the mastery level disciple (skill lvl 6) and I was able to unlock every lock I found immediately until now. You can find the lockpicking skill where you're spells are -the button on the very right is for skills. Drag and drop the icon to the hotkey bar and by pressing the hotkey and then right-clicking you acitvate it. Then click the lock you want to pick.
I think its much quieter too if you want to steal something.
Ah and by destroying the lock with bow you're very safe not to be hit by eventual traps.

How do you display HP?

its floating text. Only the Paladin can see the AI hp with a specific skill

You don't. I'm talking about red letters that start displaying above enemy / item, indicating you're damaging it.

What about the rusty key in the mines? I ended up smashing the doors down anyway because I couldn't get the key to work on them. Was I using it in the wrong place, or just not using it the right way?

how to open the chest in the room with the king's harlior ghost?

He should give you a quest, and when you finish it, chest gets unlocked.

when i came to him i had already the quest from the orc chief to kill the king. had no other options in the dialog exept of attack him. is there no ways to open the chest now? i can't even damage it with weapons or magic.

I don't think there is :-/ It's weird tho, I could have helped the king in that dialogue.

what was in the chest?

just press T to shift your cursor to attack mode, and click on what you want to "open"