The first one is fine but would also be fine with 'who'. http://www.quickanddirtytips.com/education/grammar/who-versus-that The second one is incorrect.Two possibilities: What are you most angry about? What/who makes you the most angry?

someone WHO cares about me. We can't use THAT with people and the second: the expression is get/be angry WITH.

I see yours true, but let me add my suggestion: I finally found someone who feels solicitous about me. what makes u angry at most?