Hi AnonUK,

1) He once said "We feel first and then try to map our feeling to the facts around. If am angry and feel angry I will try to find something to match my feeling".
Feelings = facts, where it's the other around for non's feelings are followed after the facts.
2) We have spent so many days together ... .You are just a part of me ... .You are like a organ of my body.
Enmeshment, not knowing your boundaries and where you end and the other person begins.
Later someday he just told me " If you don't pick up the phone, the first thing that comes to my mind is that you are with your boyfriend and that thought just blows me up so I don't call you". "I know that there is a possibility that you are doing something else but in my mind the first thought is about your boyfriend and the thought troubles me a lot".
I'd say that this is a cognitive distortion or twisted thinking, specifically catastrophizing adjacent with low self esteem and low self worth, I'm not worthy enough, she probably wants / deserves someone that it better than I.
) for me everything is either 100% or 0%. There is nothing in between. I am digital either 0 or 1
A core criterion of the disorder, all of nothing thinking or black and white thinking.
My question is - When he himself says these sentences, does it mean that he understands his thoughts at least ... .Is it a good sign ?
We can't tell what someone else thinks, how I read the things that he said is that he's articulate, he gives me the impression that there is some self awareness but I don't think that he is consciously connecting it all together, this is his reality, it's normal for him, he doesn't have anything else to compare it to, I wouldn't puy it on yourself to teach him the other side of the coin, I agree with AlternateReality, if he is BPD, I would leave it to professionals to help him unravel the twisted thinking and teach him tools to cope, BPD is a serious mental illness. I completely understand your logic and motivation, you want to help him, all we can do is use the tools and if the tools don't work then at least we tried. I hope that helps.
More on cognitive distortions.
Ten Ways to Untwist Your Thinking - Burns MD