Well question 2 I've heard lots of times and have asked this myself. I would say, if you’re asking the question, then you are not mentally ill. Most mentally ill people have no idea of their illness. Their mental illness does not allow them the comprehension to understand what mental illnes even is.
With reference to Empathy vs over sensitiveness I've found that if you suddenly feel an emotion you have no reason to feel then this is Empathy. For example your standing at a bus stop feeling fine and happy, other people arrive at the bus stop but they are no bother, suddenly for no apparent reason you feel angry or suddenly overly happy. Any emotion that you feel suddenly and you don't know why.
With sensitivity though this would be like this: your standing at the bus stop feeling fine, then suddenly people arrive and start to invade your space making you feel 'how dare they invade my space', 'why does no one pay me and my personal space any attention', 'I feel a victim' - this would be oversensitivity.
With question 1 lots of things can be truth at once because life isn't purely black and white. I've always worked decisions on the disappointment factor when I've not know what way to go. I.e. what decision would I be disappointed if I made.
I hope this makes sense to you