There is not much to illustrate regarding the operation itself: pick two points on the curve P and Q, draw the line through them, find the third point of inters

There is not much to illustrate regarding the operation itself: pick two points on the curve P and Q, draw the line through them, find the third point of intersection with the curve (which may be the point at infinity, in which case P+Q=0) and reflect it through the x-axis; that is your sum. I think Wikipedia has this visual description in the Group Law subsection of elliptic curves. Now visualizing properties of the group law convincingly, such as commutativity and associativity, that is a challenge! I am not sure what you are looking for in a subtraction. Like in all groups P-Q is perfectly well defined as P+(-Q), so as before: first reflect the point Q through the x axis to get -Q, and then connect that point to P to get -(P+(-Q)), and do one final reflection to get P+(-Q) which is the only consistent interpretation of P-Q.