Woman born and married prior to 1956 is eligible to claim property ?

Under the Hindu Succession (Amendment) Act, 2005, the daughters are entitled to equal inheritance rights along with other male siblings, which was not available to them prior to the amendment.

According to the new Section 6, the daughter of a coparcener becomes a coparcener by birth in her own rights and liabilities in the same manner as the son. Further  supreme court also in various judgment held that Hindu woman entitled to equal property rights:.

Further regarding your second query ownership of property can be by personal acquisition, bequest and succession. A mentally handicapped person cannot enter into a contract to acquire property. A mentally handicapped person can be a beneficiary of a gift of property.As the law stands today a mentally handicapped person is not disqualified from inheriting property in any system of law. However, under the eyes of the law, the person with MR cannot manage his property. 

Others can manage the property of a person with Mentally Challenged in two ways- 

When along with the grant of ownership, provision for the management of property is also made. For example, by creating a trust in favour of the challenged beneficiary, by which the trustee would take charge of the management and deal with the trust property as carefully as a man of prudence would.

When relatives of a person with a mental handicap apply to the court stating that as that person is incapable of managing his property, a manager for the purpose should be appointed.

Transfer of property can be by interring vivo. Disposition of property is regulated by the principles of contractual capacity. Section 7 of the Transfer of Property Act 1882 permits only persons competent to contract to transfer property. For all transfers of property whether it is for consideration as a scale mortgage lease or out of love and affection as a gift, the principles of contractual capacity will apply.