Also my parents don't have any health insurance. Please suggest a plan for them as well.

Father (61 years) : No Diabetes, No BP

Mother (58 years) : Type 2 Diabetes and Hypertension

Both have mental health disorders but with regular medication and care, they have been leading steady life.

1. I will suggest Max bupa reassure or HDFC ergo optima restore for yourself. But you have to wait a few months before you should submit your porting request. You can consider them for your father too but separately.
2. For Diabetes and Hypertension HDFC optima energy is the best one as it cover those diseases from day one. But the premium is quite high so won't suggest a floater for both parents. Unless you want to pay the high premium take separate policies both of them.
3. Just mention the mental health conditions while applying & I think most the insurers will approve the proposals.

Hope this is helpful.