Does Edgar ever realized that Catherine never truly loved him? Or does he love her despite the fact that he knows she does not return his love?
You seemed to have jumped to a conclusion here - are you sure that Catherine does not love Edgar? Chapter 9 is a very key chapter for this discussion, where Catherine discusses her proposal from Edgar with Nelly Dean and talks about how she feels about both Edgar and Heathcliff. It is well worth the pains to examine what she says:
My love for Linton is like the foliage in the woods: time will change it, I'm well aware, as winter changes the trees. My love for heathcliff resembles the eternal rocks beneath: a source of little visible delight, but necessary. Nelly, I am Heathcliff! He's always, always in my mind: not as a pleasure, any more than I am always a pleasure to myself, but as my own being.
We can see by this comparison that Catherine does love Linton, but that she has a very different kind of love for Linton than she does for Heathcliff. It is well worth examining this "love" that Heathcliff and Catherine have. In its description it is made out to be very intense and surreal. Remember that their love is never consummated. It is almost as if their love is parasitic - it causes them to wound each other and to drive each other to extremes.
Of course the depth of their connection is what forces Heathcliff and Linton to a stand-off and results in Catherine's death.