Destiny and fate
Klara is somehow destined for her fate, although she doesn't know it, and her grandfather doesn't understand it completely either, but he wanted to pass along the carpentry skills of his family trade, so he teaches Klara when Tilman runs away. That means that later in life, Klara is competent and able when it comes to carving, wood-working, and art.
The trades themselves (wood-working and carving) are metaphors for destiny and fate, because they imply "being shaped" by an artist so to speak. Klara in this case has been "shaped" into a certain character so she can serve a specific function—to memorialize the dead of WWI.
World War I, and the value of memorials
The time of World War I should be remembered, Klara believes, by Canadians and by the world. Why? Because as the novelist points out, each young man who died was a real human being whose lives were rich and meaningful just like the rest of us. For some reason, it seems difficult to remember that the past actually happened.
That problem is at the center of this theme. By making the main character work so hard to memorialize her loved one who died in WWI, the reader is made to understand why memorial would matter so much to someone like Klara, from whom the War took so much.
Grief and mourning
One way that the novel depicts mourning thematically is when Klara carves the face of her lover Eamon into the statue at the memorial of Vimy Ridge, which really exists by the way. The idea for Klara was to find healing by providing a more permanent legacy to Eamon. In other words, it's like a way of cherishing his memory.
Klara does a lot of mourning though, throughout the book. She witnesses some pretty serious brokenness in her family, and when her brother disappears, the family is distraught. When she loses Eamon, she decides to never marry again, and she lives a life of solitude and regret for a long time, until her brother comes home. Then she can grieve and move forward, since she is no longer alone.
