Gift deed and stamp duty on transfer of 1/3rd share in flat

Ji, you have purchased house in the name of your wife and your mother.  so only your wife and your mother are owners of the property though you invested your money. Now get a Gift Deed from your mother for 1/2 share to you.  The stamp duty shall be payable on the Market Value of her share.  But there is a fixed stamp duty for Gift Deeds in favour of Family members.  don't worry. stamp duty is less.  so get a gift deed from your mother.  if she died intestate, all her children including you have equal rights for her 1/2 share property.

1. Will stamp duty have to be paid by me only on the 1/3rd share that is going to be gifted to me by my mother? Or on the whole market value of the flat?

;;;;;;; you have to pay the stamp duty for the value of share your mother is transferring and not for the whole of property. As only 1/3 rd chare is in transaction.

2. Will indexation rule apply while calculating the stamp duty? What is the stamp duty payable in Mumbai Maharashtra

;;;;;;;;;;;;;;;;;;;;;;;;;;;;you can chec that with local courrt stamp vendore

3. What happens if my mother passes away? Can my siblings stake a claim to her 1/3rd share them being their legal heirs along with me

Yes certainaly if your mother paased away without any will or other valid transfer dopcument then your other siblings have right to calim in their mother's share.

Your mother can make a will deed and you need no stampduty to be paid ,just register that that is also a legally valid document.,though gift deed is more specific and hassel free