Mostly true.
- Did Galileo teach scientific theories which were not yet proven?
Indeed. In 1632 Galileo published "Dialogue Concerning the Two Chief World Systems". In it he presented a fictional dialogue between proponents of heliocentrism and geocentrism. However, he was merely repeating the same inconclusive or false arguments that had been debunked or questioned previously by several prominent geocentrist scientists such as Tycho Brahe.
His book can be viewed as a late response to the 18 arguments against heliocentrism that Francesco Ingoldi had sent him several years before. However, while with the hindsight of today's knowledge it may seem obvious that Galileo was right, most of the arguments against heliocentrism could be explained away with alternative hypothesis, but none of those hypothesis could be substantiated with evidence.
The main argument Galileo tried to provide in support of heliocentrism was that he argued that the Earth's movement was responsible for the sea tides.
Historical writer E. J. Aiton states that the discourse "is among the least successful of [Galileo's] investigations and completely misrepresents the phenomena it is supposed to explain,". (Aiton, E.J. “Galileo’s Theory of the Tides.” Annals of Science 10. 1 (1954). 44-57)
He also tried to answer common criticisms of the heliocentric model, such as why objects didn't fly off the surface due to centrifugal force. Galileo's argument was that the Earth is spinning too slowly to notice the effect, since it takes a whole day to complete a turn. However, other scientists correctly calculated that despite this, tangential velocity at the equator is more than 1500 km/h. Before Newton's gravity, there wasn't any explanation that could make those numbers believable. He also developed the first theory of relativity, which, like heliocentrism, was right but he couldn't prove either conclusively.
The main obstacle to heliocentrism was lack of stellar parallax. In 1588 Tycho Brahe presented his Tychonic system, which was not discredited by the Galileo observations with the telescope and still had a motionless Earth in the center of the Universe. Although it was known then that lack of stellar parallax could be explained if the stars are nearly infinitely far away from us, that was considered unthinkable back then, and no copernican follower could explain that until the XIXth century.
So the only advantage heliocentrism offered over geocentrism was a slightly less mathematically complex system (only slightly because without elliptical orbits at variable speeds, Galileo still had to resort to epicicles), but at the cost of a system which contradicted pretty much any intuition and observable phenomena known at those times. Heliocentrism was gaining supporters slowly thanks to scientists like Kepler, whose elliptical orbits provided a vastly simpler explanation to planet movements, but, incredible as it may sound, the first proof of Earth's movement didn't came until 1727 with the discovering of light aberration by Bradley, and stellar parallax wasn't confirmed until a century later.
- Is this the main reason why the Catholic Church prosecuted him?
He was prosecuted for publishing a book, yes, but not because the theories discussed in it weren't yet proved (though, they weren't, see point 1), but because he had been forbidden to espouse heliocentrism as a real thing.
Although initially published without any problems in 1543, Copernicus books and the copernican system had been banned in 1616.
The immediate result of the 1543 publication of Copernicus's book was only mild controversy. At the Council of Trent (1545–63) neither Copernicus's theory nor calendar reform (which would later use tables deduced from Copernicus's calculations) were discussed.(1) It has been much debated why it was not until six decades after the publication of De revolutionibus that the Catholic Church took any official action against it, even the efforts of Tolosani going unheeded. Catholic side opposition only commenced seventy-three years later, when it was occasioned by Galileo.(2)
It has been much debated why, but the main reason seems to be the religion wars that would ravage Europe for nearly a century. What started as a mere scientific hypothesis could be taken as an argument to disprove the literality of the Bible and then starting a new doctrine. In a time where no real separation between religion, science and state existed, this would mean war. Literally, with cannons and armies.
Galileo had had several interviews with the Pope, who invited him to publish a book comparing the two systems, heliocentrism and geocentrism, and suggested to include the Pope's own opinions in this book, but he should stay away from suggesting that heliocentrism was anything else that an useful mathematical trick to calculate the orbital movement, never an actual depiction of reality.
Galileo, however, wrote that book making a clear assumption that heliocentrism was real, and to make things worse, put the Pope's words in the character of Simplicius, who despite being named so because of a philosopher used in Aristotle's books, sounds very much like "simpleton" in Italian, and indeed spoke like a fool.
So, actually, he was arrested by flagrant disobedience, not because the Church opposed his theories - even if they remained unconvinced. Curiously enough, the Church was siding with the prevalent scientific consensus of the time, which was geocentrism.
As for the reasons for the Catholic Church to forbid him to present heliocentrism as something real, were many and quite sound. Postulating a novel astronomic theory and hence creating a new religion because of, was not only not uncommon, but almost inevitable. Several people had lead revolts in the name of a new interpretation of the texts of the Bible, in some cases starting with espousing a new discovery which contradicted the scriptures - if the discovery was a real thing or not it wasn't that important -, and the biggest of them all, the 30 Years War, was in all its rage right then. Several influential people, including nobles close to the king of Spain were accusing the Pope of not being stern enough in prosecuting those who, in the name of science, were disseminating falsehoods against the true religion (his own, obviously). The Pope couldn't risk loosing the help of the catholic kingdoms in the middle of a war, nor the risk of somebody using the teachings from Galileo, Giordano Bruno or anyone else to divide even more the christendom.
It is worthy to note than protestant movements thought pretty much the same about it. In his 'Commentary on Genesis' John Calvin said that
"We indeed are not ignorant that the circuit of the heavens is finite, and that the earth, like a little globe, is placed in the centre." (1)
And remember that Giordiano Bruno was burnt by the Catholic Church only because he managed to flee from Helmstedt before luterans did it. Luter did not approve heliocentrism either:
"This is what that fellow does who wishes to turn the whole of astronomy upside down. Even in these things that are thrown into disorder I believe the Holy Scriptures, for Joshua commanded the sun to stand still and not the earth" (Donald H. Kobe (1998). "Copernicus and Martin Luther: An Encounter Between Science and Religion". American Journal of Physics. 66 (3): 190)
So, as a resume, theologian Thomas Schirrmacher argued:
Contrary to legend, Galileo and the Copernican system were well regarded by church officials. Galileo was the victim of his own arrogance, the envy of his colleagues, and the politics of Pope Urban VIII. He was not accused of criticizing the Bible, but disobeying a papal decree. (3) (Emphasis mine)
