That might not upset Clark as much as she thinks, seeing as how he's died twice himself already. The manner in which other!Clark died might be hard to take, but overall, he could probably deal with it.

As for what he won't talk about, honestly, given time and circumstances, there might not really be anything he absolutely won't discuss with Kendra. Circumstances are very important there, though. What would be the hardest to get out of him is pretty much anything to do with Jor-El. He'll be vague or talk around it if he has to, but he won't get into specifics. This category actually covers a lot.

Second to that, probably most things that have to do with his personal life, simply because he thinks that should be private. But then, as she's already seen, he's not above throwing out something he normally wouldn't say from time to time just to get a reaction.