Sorry, didn't see this post until now. Welcome to NA!
maybe some of your questions have been answered...maybe not.
In my experience, some people usually will take a few minutes after the meeting to talk to a newcomer, welcome them, make sure they have phone numbers, pamphlets, lists of meeting times etc.
After you've tried out a number of meetings in your area, you will likely find there is one that you feel "at home" at. It meets at a time and place you can attend regularly (so you can be active in it) and it feel like your group.
Then you tell the secretary after the meeting (or the chair) that you'd like to make this your home group and in my area you signed your name and put your number on a sheet, and that was that. Once I chose a home group I made an effort to help out that group and get to know people in it.
There are many ways to find a sponsor. The general rule is, after attending a few meetings, find someone you feel comfortable with, who's shares speak to you and who has "the recovery you want for yourself" and ask if they are taking sponsees.
I think a nice approach is to open a conversation after the meeting with a person you are interested in and mention that something they shared helped you, etc, and then
Many people ask a few of the people they've gottten to know if they can recommend anyone as a sponsor. Or you could request the chair at a meeting to ask during the meeting if anyone is open to sponsoring, then after the meeting approach someone who said they were open.
It really happens all different ways. My two sponsors found me...go figure.
Awesome on your clean time and welcome to the family!