Having read comments and question I have to say I'm getting quite a different view of this than some people seem to.
My best friend and I (both male) were debating about going on a weekend trip next week. After a long talk, he finally said that he should leave his girlfriend for 2 days to be with me.
So no problem.
Just one hour after that, his girlfriend said that it's been 3 years (they are together since that time too) since she's always thinking about suicide.
She didn't threaten suicide, she apparently just mentioned it. There's no hint here or in your comments that it was a threat (you actually state it was not a threat in a comment).
So actually this could be interpreted as someone simply expressing how important their significant other is to them.
You don't even say she demanded he not go on the trip or take her along.
THere's actually no problem with her actions as far as I can make out.
Now he doesn't spend time away from her because he feels guilty when he leaves her alone.
That's his guilty feeling, not hers.
In a practical sense it sounds like he's as much the problem, if not all of it.
He probably should go on the trip simply so they do spend time apart and learn it's quite possible and reasonable to. But there is no hint in your remarks that she has a problem with this at all. Only that he has a problem with it.
I'm not saying that his girlfriend is lying, that's not the question, just that he should leave her for some days because he has no social life anymore since she is not okay with letting him go without her.
Did she say that ? That's not what you said. And your comments seem to contradict this. She didn't make a threat. She doesn't seem to have made a demand.
And, incidentally, people in long term relationships often do fall into patterns of not going out often without each other. I think you may be reading far more into this than is actually there.
How can I point out everything that's wrong with his approach, since he is always complaining that he can't do anything without her?
How much of that is his feeling guilty for no reason ?
Is she actually a problem ? It's certainly at least ambivalent from your question and comments.
Have you considered that he may be the one who is reluctant to leave her alone ? Maybe he's blaming her for this, when she's quite innocent. I have a friend who tends to cut his (rare) evenings out with the lads short and I think it's down to his own sense of discomfort at not being comfortably at home with the wife. Some blokes like their domestic role more than they like to let on.
All of your negative information on her seems to be from him with one exception :
I already saw her becoming crazy because an ex female friend (not gf) was talking to him
I have news for you : current girlfriends don't like it one little bit when you start talking to your ex-girlfriends.
Unless she pulled a knife, started throwing objects or committed an actual assault (when sober - drunk doesn't count for judging her general mental state) then this could be just simple jealousy and not in the least unusual.
Frankly you could be building a mare's nest out of nothing.
I think you need to step back from this and reconsider what you really and reliably know. Not just what your friend tells you, but what you can independently vouch for and which you know all the facts about.