Rental income

yes, agreement was made.

1.parents  will show the income under the head income from house property and can claim property taxes as well as standard deduction from the rental income 

2. Son will claim hra by giving rent receipts and showing the agreement to his hr ..... Or if not job then by 80GG

As both enter in rent agreement not gift deed or gift agreement  they  both can claim Deduction and cannot be Termed as relative rather than landlord and tenant 

The portion in which the son is staying shall be shown as let-out and rent received from the son shall be shown as Income from House Property and standard deduction at the rate of 30% u/s 24 can be claimed.