Firstly, thanks to Maggie N. for the research of Tekla's ancestors.
That research uncovers the answer to how Chopin and the American general are related.
Tekla Krzyzanowski Chopin was the mother of Frederic Chopin.
Tekla was the daughter of Jakub Krzyzanowski. Tekla had a brother. The brother had a son: Wlodomiericz Bonawentura Krzyzanowski, the American general in question.
According to the research done by Maggie, that is no "cousin" in quotes, unless there is a question as to whether unnamed Krzyzanowski, Tekla's brother, was really Wlod's father.
Otherwise, Wlod was the first cousin of Frederic Chopin.
As to manner of death, what I read from multiple sources indicates uncertainty as to whether Frederic Chopin died of heart problems or TB. The Wikipedia link attached to his bio includes a statement from Chopin himself that his throat and tonsils were hurting him at one point. That link and other sites I read indicate he suffered from poor health throughout his life.
For manner of death, maybe it could be said that he died from TB and that this is what was on his death certificate, but that questions exist about this?