As a black belt in BRAZILIAN JIU-JITSU, you can understand the finer principles of the sport; you should be able to spar with anyone using technique as the focal point, and you are able to understand or at least adapt to any style before you. Black belt is a goal for many, but when reached it is just the beginning of understanding the deeper aspects of BRAZILIAN JIU-JITSU. A black belt typically will not change their whole style—they will likely become more efficient at their style and should be able to adapt and change when necessary. A black belt should be able to independently examine their game and the game of another with a higher level of understanding. A white belt may look at two black belts sparring and see two whole bodies moving, while a black belt may see the details of individual hand or a foot placement or look deeper into the strategy at hand.
Each school or affiliation's belt ranking test will vary to some degree. Some schools may also want you to know street self-defense principles. Belts don't matter to some people but to many others they do. Belts can be a form of currency for instructors and their programs. What I mean by this is that, generally speaking, most want to learn any type of martial art from a black belt and ultimately would like to become a black belt himself or herself. Having a higher belt will typically earn you more students. Yet, it does not necessarily matter what belt you are when you are on the mat—everyone is measured by skill. So, to finally answer this age old question regarding how long it takes to get a black belt: it will take you likely between six and twelve years depending on your affiliation and your dedication level.
One more consideration that should be highlighted is competition. Some affiliations want their students to compete and may rank students according to how well they do at certain competitions. I do not believe this is essential, but it certainly can be a factor depending on your program's criteria.
There may be rituals or ceremonies at your BRAZILIAN JIU-JITSU program upon receiving your belt and moving up in rank. Some affiliations may conduct a positive speech about the student and talk about why they deserve to be at the rank they have been awarded. As crazy as this may sound, some schools have a procedure where they will whip you with a belt as you go down a line of people in a group. This resembles something known as a 'Gauntlet.' More and more academies are making curriculums rather than relying on an instructor's discretion and will have you perform a set of movements to test your efficiency and knowledge and thereafter you may receive your belt in ceremonial fashion. I would not spend too much time concerning yourself on what belt rank you are, just worry about learning and getting better at BRAZILIAN JIU-JITSU. But again, do as you choose—sometimes motivation such as a belt may give you incentive to become better.
In No Gi, belts may not be awarded. Some No Gi programs may also offer a rash guard according to the BRAZILIAN JIU-JITSU belt system. In terms of attire for No Gi, tight fitting shorts and short or long sleeve shirts can be worn. More typically, a long or short sleeve rash guard will be worn on top, similar to a surfing rash guard. For your bottom, you will likely wear grappling shorts, which are similar to beach board shorts. Specific grappling shorts often allow for crotch room or elasticity to move around and not rip your shorts. You cannot grab clothing in No Gi grappling, so sleek fitting clothes work well. Some will also wear sweat pants or Gi pants while grappling in No Gi. It seems some schools are trending to make you wear their own attire for uniformity.
Never ask for a belt from your instructor. This is often seen as begging and can get more time tacked on depending on who you ask. If you want to talk about rank with your instructor, it is okay to ask them what they look for in a particular belt so you can understand their criteria or what you should be seeking in terms of your development. Trust that you chose an instructor who is there to help you advance. Trust if you are not getting your belts right away that your instructor understands what it takes and see areas where you need progress. There is usually a lot more that goes into getting a rank/belt than just knowing techniques and "beating" your sparring partners. You have to use the techniques correctly and transition with fluidity. Earning your belt is good, but caring about learning and progressing while earning your belt is even better.