Muslim's property

Hi All,

    I am planning a buy a plot in bangalore. Here is some backgroud,

1. Property acquired by Muslim man in 1982 from Hindu owner
2. Muslim Owner have 4 kids (3 daughter and 1 son).
3. Muslim Owner died in 2010
4. The 4 children of the Owner (all around 50+ age) paritioned the propery 1/4 each in 2011.
5. The 4  children of the Owner have many kids (they are grandchildren of original owner).
6. Now the muslim owner children (1 son and 3 daughters) are selling the property to Hindu (me)

Questions:

1. Since current owner(s) are muslim's which property law we need to follow to sell the property?
2. Do we need signatures of the grandchildren of the Original owner for the sale deed registratiion?
3. How many years EC we need to check (20,40, 75 ...). We have records for 45 years?.

Please help me.

Thanks

Shashi