Can someone's natal chart show how someone is empathetic? Or if they possess empathetic abilties?
I would be looking for the water element, either planets and points or water house emphasis, 4, 8, 12.
For general outlook, I would look at both Chiron and the nodes.
Another thought, some people become or just are innately empathic with certain life issues. As an example, someone may not be at all empathic about marital problems, but they are truly understanding and can provide endless help and support about health issues.
I have Sun conjunct Neptune, north node conjunct my IC, Chiron in Cancer opposite my Sun. Would that give me empathic qualities?
"Empathy" is generally given to Pisces/12th/Neptune, if you're taking it to mean that you feel someone's feeling along with them. There's no barrier.
I've had people treat it as such, especially when I was younger and I was called too sensitive by teachers and the like. Even today, people seem to think I'm too kind-hearted as a flaw.
@purplestargirl Being kind-hearted isn’t a flaw. You just have to be discerning in who you gift your kindness to. We can’t rescue every stray cat out there. Sometimes allowing people the chance to figure themselves out of their own messes is the greatest kindness we can show them.
@purplestargirl I said I feel you before, I do 
As a highly sensitive person, I've had to hear a lot "you're too sensitive" and thought a lot about it. Why do people say this? In reference to what is someone too sensitive? And what if I'm not too sensitive but the other is too harsh? And since when being too sensitive is some sort of a having a weakness/ flaw? All arts are full of sensitive souls... I've decided not long ago that being too sensitive is one of my superpowers because I think it is.
I think being kind-hearted is a precious gem 