Can we take Health Insurance and Critical Illness from two different companies?

[CONFUSED]

1. In case a critical illness occurs like first heart attack will i be elgible for payment from the Bajaj Policy as lumpsum as well as claim all hospitalization expenses from Apollo

In Critical Illness - the policy would pay you lump sum amount, if you have diagnosed with the disease. But their is one condition here (check the policy wording in the policy - may very) - "The benefit amount is payable once the disease is diagnosed meeting specific criteria and the insured survives 30 days after the diagnosis"
In Heath Insurance - you can claim hospitalization without any such condition.
Both the amount is payable to you are independent to each other.

2. Do i need to inform each of the companies about the other policy?

If in the proposal form the insurance company asking, pls mention in details. Their is no legal requirement to inform.

3. Can you suggest any other options instead of going for 2 different policies?

I would go for Apollo Munich (old name - Apollo DVK). They are specialist in health insurance.