Can Katherine compel your character? Talk to me first before doing any of these, as altering Dilandau's mind might cause his alternate persona to break free. Memory erasure would definitely do that.

Can she bite your character? Yes, but be aware that Dilandau would feel incredibly violated due to childhood trauma involving lots of injections.

Could her blood heal your character? Yes

Is your character able to injure her? He's got a sword and he knows how to chop heads, but he only has human speed and strength.

Is Katherine able to injure your character? Yes

Could Katherine come and meddle with your dreams? It's dependant on how meddly it is, like with the mind commands. If she's seeing them, she could see anything that has to do with this persona, but all of his alternate persona's memories and dreams are inaccessible at the moment.

Would she notice anything strange about your character? His uniform has a faded smell of a liquid metal that doesn't exist on Earth.