In reference to your query:
1. There is no requirement for you to register as a proprietorship and you can work under your own name.
2. You can receive the remittance in your Savings Account.
3. Since you are an Indian Citizen as on date, your global income would be taxed in India. Also otherwise the freelance income is being earned by you in India only. Normal tax provisions would apply.
4. Yes your assumption is correct, as exemption is provided to service providers from registration in case of receipts below INR 20 Lakhs.
5. Based on the facts available, there does not seem any further complications.
Please connect in case of any further queries or detailed clarifications.
Thanks & Regards,
CA Aditya Dhanuka.