Can the share transfer on the basis of power of attorney ?

Ans: She can gift you the equity shares, when you make the sale of shares , the cost value of shares will be the value at which your wife has bought the shares and not on the transfer value while gifting the shares.

Ans: you can transfer it online through cdsl portal (https://www.cdslindia.com/Footer/Easiest.html), tax implications are same as when you transfer, its consider sale for you so accordingly short term or long term capital gain is applicable on category when you had brought.

Ans: Yes, transferring equity shares from your DP (Depository Participant) to your son's/daughter's DP (Depository Participant) as a gift is possible. Here's a breakdown of the costs involved:

Charges:

DP Charges: There will be transfer fees levied by your DP for processing the off-market gift transaction. These charges vary depending on the DP and the number of shares being transferred.
Stamp Duty: In India, a stamp duty is applicable on the gift deed. The amount of stamp duty varies depending on the state where the gift deed is registered. The recipient (your son/daughter) would typically be responsible for the stamp duty.
Taxes:

Gift Tax: As of May 2024, there is no gift tax levied in India for transfers between parents and children. This means your son/daughter will not have to pay any tax on the gifted shares.
Additional Costs:

Transaction fees: There might be minor transaction fees associated with the delivery instruction slip (DIS) submitted for the transfer.
Here's what you typically need to do to transfer shares as a gift:

Gift Deed: Prepare a gift deed mentioning the details of the shares being gifted, your son's/daughter's details, and your relationship.
Delivery Instruction Slip (DIS): Fill out a DIS form with the DP containing details of the shares and your son's/daughter's DP information.
Stamp Duty: Pay the stamp duty as per your state's regulations for the gift deed.
It's advisable to consult your DP and a tax advisor for the latest information on specific charges and any procedural updates. They can guide you through the process and ensure a smooth transfer.