Unfortunately, the main suggestion when it comes to addressing relationship issues is to communicate about them, something he's made it abundantly clear he's not willing to do, and even makes you apologize for trying to talk about (what kinds of things does he have you do to "make up" for talking about these issues?) And when that happens, it's a sign that the relationship probably isn't stable long term. After all, how are things supposed to get better if one half of the people involved isn't willing to talk about the issues?
But more than that, this isn't sounding like a great relationship for you, period. This is someone who doesn't show or receive affection in the way you do, and who you're not able to share any negative emotions around. And someone who calls you slurs on a regular basis. Now, if you were both on the same page that those were teasing words, or words that you'd reclaimed for yourself, the situation might be a bit different. But as it stands, he's calling you names when he's upset, something that a respectful partner takes care to avoid, even when they're angry.
Something that might be helpful is to take a look at this article: Potholes & Dead Ends: Relationship Roadblocks to Look Out For
. As you're reading about the different issues, also take a look at the side bar that has the recommendations for how to make a relationship better. Do you think he'd be willing to do any of those?