Hi
1) In general there will be an adoption deed for adoptions and the same may be used for claiming family member certificate by your wife.
2) If there is no adoption deed, then you can use your wife's school records( xth, xii etc where name of adopted parents are generally mentioned) as proof of adoption.
3) Even your marriage invitation card (wherein the names of adopted parents are published) can be used as valid proof of adoption in absence of adoption deed.
4) You should file for letters of administration of the properties(400 square yards , 2 single BHK Homes) in the court and obtain letter of administration.
5) In general prior to issue of letter of administration courts will implead other legal heirs (your mother in law's relatives) as opposite parties and if they have any objection, they can submit the same in court.
6) Legally your wife is entitled to succeed to all of the properties of her adoptive mother. (assuming she is the only child).
Hope this information is useful.