In general, being believed to have been authored by an apostle was a pretty strong mark in favor of inclusion in the canon. Jude might not be a high-profile apostle, but he was an apostle and, per the letter, he was a “brother of James” (often identified as Thaddeus). Moreover, according to Eusebius, he was said to be “a brother of the Lord according to the flesh”; which makes sense since James was himself a brother of Jesus.

It was among the antilegoumena, so there was some early resistance to receiving it as scripture, but that resistance was, somehow, overcome. As to how that happened, it’s important to remember the process of canonization of Scripture wasn’t linear, there was no central authority making and justifying its decision. It was, first and foremost, a largely decentralized, organic processes which gradually moved towards consensus, and that people subsequently tried to make sense of and bring some order to; it’s not like someone drew up the criteria for inclusion and then went through the books one by one explaining how each one satisfied or fell short of meeting those criteria. There were a lot of individual agents involved in reaching that consensus, each had his own reasoning and motives, so it is hard to offer a single explanation for why this particular consensus got reached.

If you are trying to understand why orthodox Christianity accepts it as Scripture, the ** you do not have permission to see this link ** gives a good overview–it’s dated and confessional, but that is probably appropriate given the question.

As to who actually wrote it, and when it was actually written, I don’t know. I would check ** you do not have permission to see this link **

“The really interesting thing about Jude to me are the references to non-canonical writings as if they were authoritative for the author.”
Yeah, that is exceptionally awkward for believers.