Partner playing "cards" in my relationship - Need advice

I am in a 3 year relationship with my partner. We live together, are engaged, and have went through "the honeymoon phase". My situation is so confusing and complicated to me. My partner was sexually abused by a family member as a child, and has been labeled as having PTSD from the experience. I cannot help but feel like he has used this horrible thing as a "card" to play on friends, family members, and me. I am the sole bread winner in the household, he draws SSI for having PTSD/manic anxiety and so on, but does not contribute to the bills. For the first two years of our relationship, I had a job that I was making a comfortable living at and it did not bother me to pay everything. I unexpectedly lost that job and I am now working a job with less income and I had to file bankruptcy after all of this. As I was going through my financial mess, my partner did not step up to even offer any help. I sold personal belongings, had to borrow money from my father to even file bankruptcy....and so forth. My job is a work-from-home customer service job, the only bill that my partner was paying at the time was the cable bill because he watched tv, he was aggrivated that I started working from home and stopped paying it without telling me - my job depended on the cable internet. I had to sell my piano to keep the cable on. He seen no wrong in doing that and it really bothered me. I am now paying everything(utilities, rent) as well as my bankruptcy(which is getting harder and harder to pay while paying everything in the household). I don't mean to write a book but feel it necessary in order for someone to understand my situation and give me some form of advice.
Six months ago, his grandmother passed away at age 97. He went back and forth on expressing his thoughts about her(at one point he blamed her for his molestation by his uncle, her son) - one moment he would say he loved her so much, the next he would say horrible things about this sweet little lady that I had come to know. At her funeral, we got back in the car and when I asked if he was ok, his response was "I made sure that one got put in the ground". I was horrified and disgusted by his behavior. Since then, he has started bringing up her death to anyone and everyone that will listen as a way to get sympathy, I believe. When I ask him for help on the bills, he says "I'm grieving my grandmother, I'm having a hard time". Our sex life has also dwindled. Where we would typically have sex every other day, sometimes more than that, it has literally been months since we have had anything other than an occasional oral act. When I jokingly bring it up that we're not having sex, he brings out the grandma card. He also says that he's not into having sex anymore, but I find him on a phone(that I pay for) watching porn and signing up for hook-up sites. When I confront him about it, he pretends he didn't know what the site was about or says he was just curious or looking for friends and since there's no "gay facebook" that was his only option. (He says he doesn't like being friends with straight people and that's why he is searching for friends on these hook-up sites). I know better than that.
He does not clean up after himself, doesn't cook, and wastes food like it is nothing. While I am scrounging in my situation, he is buying 50 dollar bottles of shampoo and so forth. I am very disgusted but I love him. I am in this for the long haul, and promised myself to do everything to make this work. His family more or less has disowned him - his mother made it clear to me to not bring him back to her house because she was finished with him. I do not want my relationship to end, but there comes a point where I will have to ultimately save myself. I am heartbroken in every since of the word. I have no clue as to what to do.