1. Does an OBE occur inside your mind like every ND or LD ?
There’s no substantial evidence that it occurs outside of the mind, so Yes is the safer presumption.
2. Is an OBE something like a LD, the only difference is that you enter yourself the dreamworld ?
But in a Wake Initiated LD, you do enter yourself in the dreamworld. Some OBE’rs may say that their OBE always paints the scene of the room they were in at the time of the OBE, therefore it must take place there, but False Awakenings often do that too and that eventually shows itself to be a dream.
What are the differences between OBE and LD ?
From my experience, an OBE is accompanied by thuds in the air whereas an LD isn’t. New Agers call these thuds “vibrations,” which was no way to prepare me for the Jurassic Park T.Rex tapdancing somewhere offscreen, so I’m angry at them.
3. Why do you have to “exit” your body in an OBE, in order to do what you want ?
If what I want is to experience exiting my body, it’s kind of the definition, isn’t it? 
Maybe some of the things that OBE’ing fulfills, can be done in an LD. A lot of other things that a lot of people want can be accomplished in-body, while they’re awake, so you don’t have to do this.
Unless what you want to do after all is try to prove that OBE’s are more than a mental experience, in which case, yeah, I suppose that would help.
4. Does the OBE have to do with spirituality and religious stuff ?
An OBE was described in 2 Corinthians chapter 12 of the Bible, and (I heard, but am less formally familiar with) probably a host of other religions’ texts. But I’ve done it myself and seen no deities or guides at all, not even met a dead person to tell me I’d breached into the afterlife, or angels to tell me I’ve been hubristic by initiating this experience under my own steam.
5. What happenes if you do a RC during a OBE ?
I haven’t been able to try. I can’t find my hands in an OBE. 
6. Can an OBE occur by itself ?
Short answer: yes.
Long answer: I think it can only occur by itself. The way I initiate an OBE, so to speak, is to go so far into mentally doing nothing that it becomes the opposite of doing something rather than the privative. Such a deep relaxation allows something else to break out. It’s like triggering a reflex, it’s not an action you can do directly, but you can do it deliberately (just indirectly.)
It can’t be a normal dream, as you must exit your own body…
So if you did already firmly believe this, why ask question #1? 
Is an OBE as safe as any dream can be ?
I would think the only people with the experience to accurately answer NO, is in no position to tell us. But I’m still alive! And Robert Monroe (in the video link answering question #6) lived to a venerable old age, that I know of, and he was having OBE’s quite frequently.
I’m not sure, but that’s what it seems it is…