There have been a couple of psychics - as well as Nostradamus apparently - say that Harry is the next King. So read into that what you will ... others have said Charles' tenure will be short (I can see the Queen living for a few years yet, so that might be why), and William's will be just as short. Most won't reveal the reason for it, but some have speculated that the Monarchy as it currently is, will end.
I don't think there was an affair. I believe that Kate and William are solid. They probably get annoyed with each other from time to time, but that's a given in any relationship. Before Rose came on the scene there were rumours about William and Jecca Craig; yet they appeared made up also. She is married and has her own child(ren?) now.
I heard that the whole affair story was made up by Nicole Cliff (I think that's her name), who posted it as a half-joke, to take the heat of Meghan and Harry.
Just because there's nowhere else to put this, I will say that I think there'll be one more divorce announcement before the end of the year - Sophie and Edward.
I don't know all the predictions and who made them, but some people have commented they have already come true: the abdication crisis of the 1930s, when "the brother who wasn't meant to be king became the king" (as one such prediction states).
With Will having 3 kids it seems highly unlikely H would ever become king.
Then there are the predictions of the end of the Windsors as dynasty and the end of the monarchy after Charles...
The Jecca rumours had some more footing, Jecca was guest of honour at Will's 21st or 25th bday (don't remember which) and was seated next to him, whilst Kate was at the end of the table. K has also dressed at times just like Jecca and one famous weekend which was a "boys' hunting trip" had Jecca included, per the pics she was the only woman (unless others joined later, but it was always claimed that it was a small party, so no others to join in). The hunting trip happened after he married Kate and after George was born.
Will also blew off Peter's wedding in favour of Jecca's brother's wedding (that was when Kate allegedly met Liz for the first time and Will wasn't even there to make the introductions) and blew off Charlotte's first Easter holiday in favour of Jecca's wedding in Africa, which he attended on his own.
Will was also after other women, trying to get together with them (one famous example is Isabella Calthrope), but they all declined so he kept going back to Kate..
There are rumours Will cheated on Kate during their dating years and their relationship started via cheating as well, cheating on their respective SOs at the time. I wouldn't be entirely surprised if he continued cheating (if the rumours of the dating years are true and I tend to think they are), but the Rose rumour is imo made up.