Hi,
Regardless of a TRV or a super visa, your parents must demonstrate their individual strong ties/reasons to return to India. The greater the dependence on you (for example, financially) the lesser the chances of getting approved.
1. Online/Paper submission: It's a matter of personal preference. Approvals would depend on the quality of the application (evidence, strong ties) and it is not impacted by the type of submission.
2. Super visa is a type of temporary residence visa.
3. There's no way of knowing if your dad will clear the medicals or not for a super visa until he actually does the medicals. His heart condition and diabetes (if it is uncontrolled/insulin-dependent/he had other medical conditions arising due to diabetes) can affect the medicals.
If you don't want to risk a super visa refusal due to medicals then your dad can do the super visa type of medical tests from a non-designated panel physician.... check if he clears these medicals.... and then actually go through the medicals for the super visa.
5. If his medical condition is affecting his ability to work then you probably have the answer already without doing "preliminary" medical tests.
6. As your parents do not have strong ties (unstable employment, no finances, no property, no travel history, etc)..... your best bet is to apply only for TRV for one parent while showing the other parent as the family tie to return to. Do not apply for super visas.
7. Your birth certificate or school certificate which has both your parents' names will help.
8. GC key on your dad's name
9. Yes, you can
Cheers