Dear Sir,
1. Yes, you can continue using this account for buying/selling of shares or any other property transactions.
2. Gift to parent will be exempt from tax in your parents hand So it will neither increase nor decrease the tax liability of your parents. It will not reduce your tax liability.
Please feel free to call/revert in case you need any clarification.
Thanks and Regards,
Abhishek Dugar
CA CS B.Com