Term insurance is there to protect your income. While it is cheaper in early years, if there are no dependents on your income (including a property that is on loan), then you don't need it. Wait till you have dependents to purchase and invest the premium for now.
For health insurance, multiple options are there. Get a personal insurance other than the one given at work that gives a good cover (healthcare costs are skyrocketing and your room rent is capped at 1% of the SI). Some banks etc. give a group insurance for all account holders, so the premium remains the same irrespective of the # claims in the previous year. If you want single room etc. ensure you get a SI of ~15L if you are in a tier 1 city, and want the best care.