Yes to all questions. In addition to Tony Dismukes’s post, BJJ is probably the best guarded and policed black belt in the major styles of MA. Many other styles and organizations in MA view a 1st dan as someone who’s proficient in the basics of the art. In BJJ, usually the person has learned and applied pretty much the whole syllabus. They’re still learning, refining, and evolving the art, but dan rank promotions are based on advancing the art and students’ learning, not like where in karate for example a 3rd dan is awarded after completing the 2nd dan syllabus where applicable.
I may be a little off. I’m not a BJJ guy. Just my outside looking in view.