As a uni student, does it make sense to buy insurance?

Hospitalization plan and a personal accident definitely. (you may already have a PA plan given by your school)

After you start earning, then look at income protection policies.

Nah, i dont think it makes sense to buy an insurance now, especially you are not earning any income and if there is already a policy which ur parents bought it for you since young(for my case).

Yes.

https://www.straitstimes.com/singapore/teen-who...

Yes, i feel that it is important to have at least some insurance for wealth protection. But also make sure you’re buying what you can afford, even though it is better to get some insurance when you’re younger as the premiums will be more affordable too.