I don't understand why you encountered a dearth of information about Crassus. The story is well known. Plutarch wrote a biography of the guy and that survives, as well as any number of comments from other ancient writers.

After his consulship in 55 BCE, Crassus got the command against Parthia, and took an army east. He chose to cross the Euphrates as soon as possible, rather than marching through the mountains to the north, and encountered the Parthian army at Carrhae in 53, where he took brutal losses and ultimately died.

Julia, Caesar's daughter and Pompey's wife, died in 54, and while that might be the start of their break, real hostility didn't become obvious until 52. Crassus had nothing to do with the dissolution of the triumvirate except the fact that he died.

Crassus lost three legionary standards at Carrhae, and recovering those standards became a major foreign policy goal first for Caesar, who got himself stabbed the day before he set out on that campaign, and later for Augustus, which he accomplished.

I'm not sure there's anything else to say, unless you have more questions?