1. Title Search means checking from the Registration office about the title holders of the said property for last 30 years. It gives clear view of the flow of the title of the property and it also ascertains whether the vendor, as per the records, is the title holder of the property or not. You can conduct the said search through a local lawyer having expertise in this field. Cautious buyers even collect certified copy of the last title deed to be sure about title of the vendor,
2. It will be difficult for you to find out whether A had only one son or other legal heirs also. Engage a lawyer for that matter,
3. The court search shall have to be conducted by a local lawyer,
4. Property is mortgaged while taking loan by depositing the original title deed. So, if you get all original link deeds from the vendor, it is established that the property has not been mortgaged.