Often dojo will offer several levels of classes. A beginner's class for new students who hold no rank, a general class for all students, and advanced classes for yudansha. From what I've seen, the beginner's classes are tailored to introducing brand new, unranked students to the art and focus on ukemi, dojo etiquette, very basic technique and various kinds of drills. The purpose is to prepare them to join in the general classes safely. Some dojo don't offer beginner's classes, preferring to integrate new students into the mainstream from the outset. You see both styles, apparently because both have their merit.
I've experienced 3 types of dojo set-ups:
1. They mix beginners and advanced students together in one class
2. They mix beginners and advanced students together in one class but sensei teaches different techniques to both groups
3. The beginners, intermediate and advanced classes are totally separate.
I like the 3rd set-up most because when you advance, you like to up the intensity in your training by attending the advanced classes. Similarly, if you want to practice kihon or test your techniques with beginners if they are really working, you can attend the beginners classes.
In the 1st and 2nd set-up, you'll feel some discrimination as a beginner but this is unavoidable imo. It's human nature.
Regarding kyu advancement, it both important and not important at the same time. It is important as this is one of the metrics how you progress as an aikidoka as seen by you and your peers. Some people however make grading as the only basis for progressing even when their technique isnt good. There needs to be a balance in how you approach grading.