I will try and answer on your points with my point of view.
1.He cares or else he wouldn't try to go back in cryo.
2.He is taking everything in strides because he has amnesia, imagine you wake up after 4 years in a hospital bed with no memories and a woman comes and tells you she is your mother, you are like "Ok" you accept that but you don't remember her or anything for that matter, so you don't feel attached to her or your sister.
3.He is fine living with a stranger because she is the first person that show that she cares for him, while on the other hand his sister is indifferent to him and cold, he tries to learn why etc. and thanks to the detective he finds out about the hacker and the timeline fits the time he went to cryo, so he somewhat "understands" why his family treats him that way.
4.His "suicide"is a bit abrupt but it is also like a "burst"of his emotions , he wakes up 4 years after with no memories and the people that say are his family seem not to care and are indifferent to him and he feels completely alone and helpless so in an emotional state of mind he thinks "what's good to be "alive"again?if he is alone and his family ignores him" thus the cryo.
5.From the latest update it seems that his mother cares for him but his sister and head of security in the company is calling the shots on how to treat him so far, it seems she is testing him to see if he really has no memories or if he is playing them, she is "cruel"because she thinks he is responsible for the hacking and probably for the death of their sister and until she is convinced otherwise she will continue with her plan.
Again "he doesn't give a rats"its more like he has/feels? apathy ,so he is also understanding , he is amnesiac after all.
Well this is how I see it
.PS.In the last update we also see in the last visit to the doctor while he kiss her he gets a flashback ,a memory of 2 women kissing and he wonders what was that , this makes it more evident that he really has amnesia and he doesn't pretend.
