After the first three, none of these men actually deserved the title as none of them ruled over the entire Muslim world. Some had dominion over significant portions of it.
Controversial but objective. Ali certainly deserved the title... but he was barred from excercizing its full powers, let's put it that way. You can think of it like an elected president by the majority of the populous who was nevertheless continuously impeached by one of the major parties who had supreme control over the minority of the states that didn't vote for him. That was Muwayia's party, for lack of a better comparison... (i know I might be mixing up government and legislature but these were the olden days... bigger army diplomacy). Yes, essentially it was a civil war, but it built up slowly over the course of his sticky five-year reign.
Oh and wait a minute... most of the Umayyad caliphs after and including Muwaiya himself, with the exception of Yazid and a couple of others (around the second civil war) did have supreme political control over the Islamic world, which was just one sprawling empire at the time. And, yes, I'm including Ibadi Oman. The big splits happened gradually after the Abbasids took over. If you meant supreme spiritual control... then that could be up for debate.
You're not. Islam as a faith wasn't widespread even within the empire's borders. It actually took several centuries for Islam to become the majority religion across the caliphate. Many regions maintained their original faith under the Jizyah system for a very long time, since their churches and institutions were largely protected, and they had no incentives to leave their homelands. That explains, for example, why there is a sizeable minority of Christians in Egypt today (about 10% of the population), and also in some Levantine countries, after almost 14 centuries of their conquest.