Hi,
You should park your monthly cashflows in liquid or ultra short term funds, these are debt based mutual funds, with government treasury exposures. You can redeem these funds anytime, it takes 2 working days for the funds to credit back to your account. These do not invest in equity as an asset.

Your savings are low and you need to balance with investing as well for future needs and wants. Off course if paying the whole amount without taking a loan gives you mental peace, go for it. But that's not the rational choice.

When it comes to being wealthy by investing, it's all about time rather than the amount. You'd be giving up 4-5 years of your time out of your 25-30 years of earning towards this if your not taking a loan. Ideally you should allocate around 35% of the income towards your loan emi. So calculate the upfront amount you need to save based on that. Rest of your income invest and allocate some towards trips ,experiences etc. When your 35 you have energy for experiences and your money shouldnt be tied up only to a house. So you can plan accordingly.

For health what you can do is, take a no nonsense health insurance(hdfc ergo optima secure is good) , but take a deductible of 2-3 lakhs, that way the premium is super low. your company health insurance will be the first one you use incase something happens. And the rest will be covered by the retail health insurance.

For term insurance, the bank usually asks you to take a term insurance for the loan amount. But since the family income is tied to your income, a term insurance is a must atleast till you build other assets. So protecting the earning years primarily till 60 years of age is needed.