No, it's not true that we had a nuclear war in the 19th century. The scientific and technical prerequisites for developing nuclear weapons were, to say the least, not available to any civilization at the time. (And there would be, to say the least, lots of evidence of it.) It is a very silly idea with absolutely no merit. The person who floated this idea is either a fool or thinks you are one. Consider frequenting better forums (like /r/AskHistorians!).

As for trees, you should ask an ecologist/botanist. It may be helpful to preface your question with whether it true or not that the trees are indeed "so young." You seem to be taking a lot for granted in your questioning based on very little evidence...