It is true that Dodi Fayed was engaged to model Kelly Fisher shortly before his relationship with Diana began; Fisher later filed a breach-of-contract lawsuit against him.
The episode features a televised debate where viewers call in to vote on the monarchy's future. While similar debates occurred in the 90s, the scene of Diana repeatedly calling the "No" line is a fictional dramatization. The.Crown.S05E10.ITA.WEBDL.1080p.mkv.mp4
In a lighter fictional moment, Prince Andrew gifts the Queen a "Big Mouth Billy Bass" singing fish, which she reportedly found amusing in real life as well. It is true that Dodi Fayed was engaged