The diphtheria is a good background, especially since Jonathan was so young during his fatal heart attack in this story.
I wonder if including the last name "Kent" on Tess's coffin was a wise idea. I could see that coming back to cause trouble.
Possible, but unlikely. She's buried 50 miles from the nearest district (and people aren't supposed to leave their districts), plus wood is biodegradable and would eventually disappear.