Sej588:
Responding to each of your questions:
• What do you guys suggest I should do to help me with my situation? Would I count as a diversity applicant?
I am not sure you will count as a "diversity" applicant, but the admissions committees will definitely take this into account as part of your overall profile and, what I imagine, is an obstacle you continue to overcome. As noted above, you should prepare for the interview as you normally would independent of your stutter.
• Should I speak to someone in admissions before the final application deadline and let them know and see what they suggest?
I do not think that is necessary. If you feel it would calm your nerves, you can put in a call and briefly let someone know that this might be a factor. The admissions committee might provide you with some meaningful advice based on their process or they may just general suggestions.
• Should I mention it in my essays and explain how although it's a weakness, it's made me the person I am today: perseverant, empathetic, and hardworking and how I can use that to make a positive impact on the community?
I assumed that this was already an integral part of your application, most notably in the essays. It won't be perceived as a weakness if you have taken steps to overcome or manage it. If it's a significant part of who you are, include it.
• Should I disclose my stutter on the day of the interviews?
You can let your interviewer know that you do have a stutter and that if xyz happens for them not to be alarmed. I don't see the harm in being upfront in a brief and professional manner. Just don't try to look like you're overcompensating in any way.
If my team or I can be of any help with your application in general or the interview specifically, please don't hesitate to reach out to learn more. A free consultation (link below) might be especially useful for you and the special circumstances you have described.
https://admissionado.com/free-consultation/