The Byzantine Empire existed in Bulgaria, Croatia, Greece, Italy, Serbia, and Turkey.
Byzantine legacy can also be retraced in
Kyivan Rus that existed in Ukraine, Belarus, and Western Russia. But it is a stretch to assume that these states represent Al-Rum.
"The Byzantine Empire was the most important basis of Christianity for centuries before the rise of the West and transmitted the cultural, legal and political legacy of the Roman Empire to Europe."
Source
Sheikh Imran Hosein used to be a reasonable scholar but he stopped making sense a while ago. Nuclear war with the US? Sure. I would like to see if the world survive this madness. There is more of a chance of the US regrouping and recovering than many states around the world because the US has a global military profile unlike any other. But a nuclear war will cut the size of mankind by a huge extent and make mankind vulnerable to extinction. This dynamic does not fit with the age of prosperity claims, right?
Hadith should be studied but actual attempts to enact end-of-times prophesies? It does not end well.