It sounds like your in a bad situation with dad , from here you seem like you are being very reasonable . Your dad very well could lack insight into his own behaviour and not see how that effects those around him .

Your right as far as children being sponges ,our personalities are composites of the people and experiences that make up our young experiences good or bad we endure good and bad .

My father was the very definition of IED , the woman i call mom was not by birth ,she adopted me and undid as much damage as she could ,well loving me and seeing in her own way nature or nurture, my birth mother was stellar woman, who unfortunately insisted she wanted kids , she turned my father's proposals down 3 times because of it , he figured this out and agreed to have kids , that was the biggest mistake of her life ,ultimately I may not have been born without them ,however as the youngest of three by the time I was 6 ,my father was an evil man ,who got tired of acting loving and let his true feelings come out including his previously fairly well disguised IED, then his bizzarre actions and occasional impulses went to 15 all the time , I became a near constant runaway rather than get beat ,I would leave ,my mom was very sick when I was 11 so I went home , 9 days after my 12 bday he blew his stack literally he murdered my birth mother and tried to kill me . He was known as the lunatic of the neighborhood for his behaviour and animal torturing and abuses of neighbors ( it was an open secret we were being abused ,many nights town cops would pick me up and look after me making sure I got to my physical safe places or taking me to sleep in the chiefs office in bad weather ) protection of children was not a priority or as unacceptable as today in 1970's .

So the psychologist who adopted me ,tested the whole concept of nature versus nurture everyday raising me , she found her answer and probably breathed a sigh of relief when I became an adult and am nothing at all like my father or family ( matter of fact his violence resulted in my becoming an IT in "AVP" ,a mediator ,and dedicating my able bodied life as Firefighter) I did inherit a mind for engineering and electronics and I look alot like him .

All that to explain if he is IED ,sure they don't all go as ballistic as mine did ,but please be carefull , you sound like your handling the added stress he places on you . Be carefull not to give any fuel to his disorder . I can't speak to not having empathy ,it's not good/bad ,I honestly think much of life is only what you do with it. Lots of people do fine with and without Different "coping" skills, and remember there are late bloomers so if you develope empathy dont consider it diminishing your individuality . We all have a general IQ & "EQ" emotional quotient , they can be vastly different from each other ,they do share one thing and that's they can both be learned ,it's not just intuition it's learning how and when to trust and use your skills.

I was once told , I can't swear by it or say it with certainty, that for every "bad" year we live it takes 2.5 years in therapy to unravel it and make sense of ,how it impacted our life. Congratulations for getting a head start on healing and for dealing with your dad and his issues , let them remain his !.