What are Trebol's powers?
I truly believe he is a Logia user, it just makes sense. I agree that he used his powers to make his mucus outer shell. I believe he activates his full Logia powers when he needs to, thereby making his coat an extension of his body. Then he refrains from using his powers to keep his real body separate from his coat so as not to be hurt by haki users. So opponents never really know what they are hitting.

I compare him to a jello mold with a piece of pineapple in the center. Hard to get to that pineapple by simple means lol.

I also agree that Law's sword was imbued with haki to hurt him. They were in Law's Room after all, so it is quite possible that he was able to gain control of his arm and attach haki.