Will 58-year-olds be denied health insurance?

If you apply for health insurance and life insurance, you need to tell your health status and past medical history truthfully, and then the insurance company will decide whether to underwrite normally, increase the cost or refuse insurance.

Common chronic diseases, diabetes and hypertension are generally refused insurance.

If you take out accident insurance, you need to look at your occupation.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.