The general gist I'm getting here is this: you've been dating this guy (W) for a year, and things have seemingly been going well. However, although he has met your family/friends, you haven't met his, and he has seemed reluctant to introduce you (even before the death of his father).
You received some difficult health news not long ago, and it sounds like he wasn't very interested or supportive, and in fact made a very disrespectful, disgusting and rude remark about getting together with one of his colleagues instead.
Lastly, since the death of his father, his communication has changed, and he now seems to be putting more emotional distance between you. This might be understandable in the circumstances, but it sounds like some of this distancing is very specific to the nature of your relationship. Not only does he not want to introduce you to family/friends, but he wants you to come to the funeral as a form of support, yet keep your distance and pretend you're not in a relationship with him? He also hasn't asked you about your own health/wellbeing, and has stopped using affectionate language.
I'm going to be honest here and say that I think he seems to want the emotional support/attention benefits of having a partner, but isn't prepared to invest in/nurture the relationship, seems disinterested in your own health/wellbeing, and is asking you to pretend to his family/friends that you are not in a relationship with him. At minimum, this is weird and unhealthy behaviour, but I would go one step further and say that actually he is being quite toxic and unfair, is an inconsistent and unequal partner, and you can do a lot better.
I particularly think this because he didn't seem to want to offer any support/love/help when you were going through a difficult time with your health, but now that he's grieving and struggling emotionally, he expects your unconditional, unquestioning support. IMO, it isn't normal to ask your partner of one year to pretend to be only a friend in front of your family/friends. Yeah, a funeral isn't the best time/place for introductions, but actually he could prepare for that. He could tell people now that he has been dating you, that you mean a lot to him, and that they will meet you at the funeral. Why would that be difficult? Unless his family/friends have a weird reason for not wanting him to be in a relationship, which I can't imagine.
At this point, I would ask, what are you getting out of this relationship? Can you imagine things recovering from here?