I can elaborate slightly. I'll provide a little context to the whole situation - if you are okay with that!

To begin, "The one key fact of the study of Bruno's life is that we do not actually know the exact grounds of his conviction on charges of heresy." - Richard Pogge, Ohio State University. Later on in that article that I'll be citing later on in this post, he comments that the majority of speculation of the specifics of his conviction were, in fact, theological. To me, this probably means your points above listed are likely, or at least reasonable to believe, to be correct.

Giordano Bruno's first faith was found in the Roman Catholic Church. However, by the time he was 18 he rejected the divinity of Christ, but kept these views private and became a Catholic priest anyway. Bruno was a bit of a loud mouth, at least in my opinion from what I've read, and at times people did suspect there wasn't something quite right about his theological views because of this but that came into play later on.

Bruno's science wasn't known for being all that great. Prof. Richard W. Pogge a professor of astronomy at Ohio State University states in his article The Folly of Giordano Bruno, "Bruno was not an astronomer and demonstrated a very poor grasp of the subject in what he did write... There is nothing in his writings that contributed to our knowledge of astronomy in any substantial way."

He continues and elaborates, "Further support for the idea that Copernicanism was likely to have played only a minor role if any in his conviction comes from the contemporary record of the discussion of this idea. What many popular accounts seem to miss is that the Church did not formally condemnation Copernicanism until well after Bruno's death. While Copernicanism was indeed a topic of discussion and controversy in Bruno's time, few astronomers supported it in 1600, and the Church itself was not to express an official opinion on the matter until 1616. By that time, Galileo's telescopic observations (from 1610 on) had completely changed the intellectual landscape, and the Church only then felt compelled to respond to the rapidly growing controversy. The issue was brought to the fore by the publication of a book by Paolo Antonio Foscarini (1565-1616) that defended Copernicanism against charges made by itinerant preaching monks that it was in conflict with Scripture, casting the issue in theological terms that the Church could no longer ignore."

Then, it is important to consider that Bruno was excommunicated by three different Churches: Roman Catholic, Lutheran, and Calvinist. These excommunications were all on theological grounds and not scientific. Which leads to Bruno being eventually turned over to the Venice Inquisition by a man he was working as a tutor for. Robert P. Lockwood, a modern Catholic author, writes in his article How Fact Becomes (Anti-Catholic) Fiction that, "Most cases brought before the inquisition in Venice resulted in acquittal. But this was different: Here was a renegade priest who faced serious charges, including outright heresy and blasphemy...His trial in Rome would take seven years. At first Bruno relied on the defense that most of his heresies were jests not to be taken seriously, but as the process dragged on he grew more obstinate. He eventually turned from what could be interpreted as negotiation over his views to defiance. He refused to retract his heresies and maintained that the judges had no authority over him. The judges had no choice but to condemn him based on his own admissions and turned him over to the secular authorities in Rome. He was executed on February 17, 1600."

Note: The Catholic Church did not technically kill Giordano Bruno, the Roman government did. I point this out because it is a common misconception. In this time period, secular governments viewed heresy as treason because, as medieval historian Thomas Madden says in his article The Truth About the Spanish Inquisition that, "It [treason] doomed the heretic, endangered those near him, and tore apart the fabric of the community." However, a secular government did not have the expertise to determine heresy. Thus, the Church established inquisitions to work with the secular government to help them determine these things.

Let me know if you have any more questions :) I apologize for ranting and getting off track throughout - but whenever Bruno comes up I like to clear up misconceptions about his case, which you may or may not personally have! I hope it is interesting regardless.