1. EMI is paid not based ownership of the property mortgaged but based on the application filed, i.e. He/she who has applied for the loan will be considered as the Borrower of the loan and shall pay the EMIs despite the fact that the mortgaged property belongs to some one else party or fully, who will be considered as mortgagor.
2. In the instant case, you both can jointly file an application for availing loan to be repaid by both of you separately in parts for which you shall keep the original title deed of the property creating mortgage there upon.
3.For your wife's paying EMIs, you won't have to convey part title of your property by registering a gift deed in her favour by paying stamp duty and registration fee which will depend on the amount of stamp duty and registration fee charged by your State Government since the stamp duty, being a State subject, varies from State to State.