Hi there, I'm sorry you are having such a worry with your DS. I have limited knowledge of teenagers, although I have just embarked on a teenage DS myself, but from what you say your son's behaviour sounds pretty 'boyish' but there's the odd thing that does concern me.
For instance, the jumping infront of you when you have the hot dishes etc. Does he realise, do you think, that you have hot things there? Even now my 13 year old DS can launch at me for a hug or just being clumsy near me and not realise I have something hot in hand. Then, if you tell him to be careful, does he realise what could have happened, what is his response? I think this is crucial to the psychological assessment, I'm no psychologist (qualified nurse and did a basic psychology course with the OU recently) but does he give an appropriate response e'g oh sorry, I should be more careful, or whatever. The other thing that would bother me is the blatant lying, all kids can pull the wool over our eyes but need to learn when they are over stepping the mark with it. Did the psychologist do a home assessment? People will automatically behave differently in different settings.
About the caring thing, I would say it's still early days at the age of 15, he's not had much experience of life yet. I would be worried if he was still uncaring in a 5 years time though. I would be too worried about the washing line and the phone thing, he could have just been inquisitive with the phone and got carried away. My DS announced that he went into the back garden to a bush swarming with bees the other night 'to try and get them to sting me', (!), needless to say we told him how stupid he was.
I hope I've helped a bit, treat him 'normally', don't put up with 'stupid' behaviour (see above) and just show him examples of caring and give him opportunities to care ( does he have a pet?). Good luck.