Should I mention that I have a Bipolar disorder in my statement of purpose?

I would not put it in the statement of purpose as it is a forward looking document (what do you want to study, what qualifications do you have, why study at X university, etc.).

If you must include it, then the diversity statement is a good place.

That being said, I would recommend that you do not include it. You can mention that you “struggled with some health/personal issues” in college but are now prepared for university, but you do not need to give details beyond that. This is your health privacy at stake. You should talk to your letter writers to make sure they know they should not disclose your personal history without your permission.

Once you are accepted, you can inquire about student health services and reasonable accommodation for your needs.

Probably not, and even from reading your question alone - with full respect to the legitimacy and seriousness of your illness - you are using it as an excuse. And in a grad school application, you are making an excuse for failing before you even start. That is not good.

Sometimes these personal facts make sense to share as part of a narrative of resilience or overcoming challenges, but you are not building that narrative right now. You need to convey that you understand the world cares more about outcome than handicaps, and, for instance, blaming psychiatrists in India, does not help.