1. Do I need a paypal account?

Yes, you need to pay using paypal service so account is required.

2. Do I need to keep track of payments?

Yes, you should. Though, most of the transactions can be viewed in your paypal account.

3. Is there any other mode of payment?

No, as of now paypal is the only way.

4. Do I need a credit/debit card for payments at paypal?

Yes, you should have.

5. Is paypal safe?

One of the safest services for financial transactions available for internet

6. Shall I connect my Account with paypal?

Read the paypal documentation, it may or may not be required if you are paying. But if you are receiving payments, yes this is required.