You may see "TT" instead of "II" because that is the way it is done in math sometimes. However, "II" is the correct form. I know that my GC name is not correct but I had few options. I wanted a lowercase name so that I could remember it and "ii" just looked too funny.
ETA - Regarding the next steps... basically, you just wait for an invitation to the next event. I know that it's hard when you are excited.
That event could be an informal coffee with just you and a couple of members or a non-business meeting. It really depends on how the chapter wants to handle it.
In my case, I had gone to a few AOII events with absolutely no intentions of joining. A good friend, who visits these boards but rarely posts, just never gave up on me. It was after one event that I realized that this was the place for me. Once I decided to move forward, my paperwork was processed in less then two weeks.
Timing was everything because the Alumnae Network Specialist was just about to go out of town and the International Executive Board was meeting 2 days later. I was initiated 3 weeks after that! It was all a big world wind of events. My mother died and my great-grandmother died on the way to her funeral. Less then two weeks later, I was initiated. (Try to find a white maternity dress in November! Thank goodness my MIL is a seamstress.) Two weeks after that I had my son.
Good luck.