I will only go through debate regarding parts that are related to the OP, and for the rest I may place only some links.
"It was not until the 16th century that a fully predictive mathematical model of a heliocentric system was presented, by the Renaissance mathematician, astronomer, and Catholic cleric Nicolaus Copernicus of Poland, leading to the Copernican Revolution"
Heliocentrism - Wikipedia, the free encyclopedia
You can't equate the claim that every mathematician in the world believed the earth was the center of the universe and a clam about a fully predictable model of anything. You are trying to salvage a mistake by qualifications. You and I know very well that is not what his claims stated. He strongly and emphatically stated that all professionals believed in an earth centered universe. It is also obvious (at least by the text YOU supplied) he was claiming that to be true from the oldest of times until the 16th century. We also both know that is not true. In fact the person even says who invented it and when. It was over a thousand years before the date you give above. Mathematicians, philosophers, astrologers, etc... believed in a sun centered universe during the entire period you mention. The statement he made was not about arbitrary models you equated with it, but about belief in an idea. Again you are desperately trying to salvage a mistake by inventing arbitrary criteria not mentioned in the statements themselves. That is exactly what happens every time a person is credited with perfection. Christian recognized that fact from our inception. That is why for your sake you did not hold that position on that text. Men will always fail us.
I
am not aware Muhammad made any mistakes.
I am sure you do not "officially". Baha'i as I have stated emphatically have the ability to simply interpret things in any way required to meet a demand. You demand he not make mistakes and will do anything to the Quran and history in order to make that occur. The man decapitated his way across the ANE, he gave the exact description given in the bible for demon possession for his initial revelations, and he himself thought he was possessed, he constantly got biblical history wrong and the mistakes he made are easily traceable to his uncles imperfect biblical knowledge, he killed for revenge, he killed to stop poets from writing unflattering things about him, he got math, science, and biology wrong. He plagiarized gnostic, apocryphal, pagan, and mythological texts that pre-existed Islam. He tortured, killed captives of no threat to him even when he admitted he had no divine instructions to do so. I can go on indefinitely. My advice test, test, and test again before you place perfection in the hands of a human. Even our greatest prophets are admitted to be exactly what they were, faulty men empowered by God, not perfect. Baha'i assumes a burden that it can't meet (even by re-writing other religions texts).
The Sun has a movement around its axes, and I am thinking that is what the movement in a fix place refers to. Movement in a 'fix' place as opposed to 'orbiting' like the earth or the moon.
Actually the sun does orbit something. I can't recall what. Almost all things orbit something even if it's a black whole like our entire galaxy does. The point is the sun is doing anything but something in a fixed place. The word fixed dooms almost anything you can say about the sun in the cradle. It isn't fixed.
What we should consider is, the fact that 'after Revelation of Muhammad', the Arab civilization rose in sciences.
That is an arbitrary and simplistic standard. Christianity rose in the sciences long after it's appointed time according to your arbitrary criteria. Islam seems to oscillate and is still making halting progress. However the theological would seem a far more rational candidate for what you stated. Islam is not only growing but the rate is accelerating. Christianity adds enough new converts in a year to populate Utah. There exists no evidence, in fact all evidence contradicts unless you haul out an arbitrary micro-scope, for what you stated. It takes a mighty thick and wickedly deceptive lens to find any truth in the text you quoted (or at least the part you did). I truly hate to see it. Your devotion is worthy of a better cause.
It has nothing to do with the number of Muslims or Christians growing.
It should. If a religion has a marked relevance that means anything then I would expect it to decline after that point. The statement is so ambiguous that I can't say exactly what he meant (neither can you). However the most obvious meaning of what he meant disagrees with reality. Even assigning his words an arbitrary scientific reference does not equate to reality. According to your preferred interpretation Newton, Galileo, and a thousand other Christians who were sciences greats should never have done as they did. Not even mangling your own people's texts will help here.
The concept is how those teachings can transform a people to become more civilized both in sciences and in human virtues. That is meant by fruits of a Tree. When a religion becomes merely based on imitations, dogmas and fanaticism, and only outward acts, and when so many sects and denominations are made and each interprets the Scriptures according to their own imagination, then that religion looses its true influence in a positive way that originally was intended. Of course that is precisely one of the main reasons that when the set time of a religion is reached, God reveals the Truth again. It is like the Process of Spring time that brings life again and again every year. It is like when the Death of Winter Comes, then Spring follows it. It is like the Night that is followed by the Day. it is Like the Sun that appears in every Morning to resurrect the Dead in Sin.
Is the Baha'i middle east or the Christian west todays civilized cultures? It is always a Christian nation not a Baha'i that is first on the scene to help with natural disasters. It is the Christian US that must mediate all tyrannical lunatics not Baha'i. It is our science and technology that drives the world. Even Israel (which by your interpretation should be technological morons by now) outstrips the entire middle east in most areas of advancement. Why didn't their time end?
I get your analogy, I just find reality the exact opposite.
According to even your interpretations:
1. Israel should have long past into irrelevance. Yet it has seen a huge upsurge in science, politics, economy, power, military might, you name it.
2. Christianity should have also passed into irrelevance yet it is still growing in theology, science, economy, might, you name it.
3. Islam should be the next to have passed into oblivion. It has self retarded it's science and economy but it's theology realm is still a thousand times what Baha'i can boast and not only is growing but growing at an increased rate.
4. Baha'i should be at the for front of technology and theology but is instead a negligible contribution to both.
Reality and that texts claims are not congruent and even your interpretation is hopelessly betrayed by history and current reality.