//What are the requirements to apply for legal heir certificate?//
Death certificates of the concerned (father or mother) with an application to local revenue authority. (Tahsildar). Copy of Family card is to furnished.
//Does applying for legal heir certificate be only possible if there is "no property" involved?//
Having property or not is not relevant to obtain legal heir certificate.
//Is Birth Certificate (with fathers & mothers name but no name of child) not sufficient proof to show legal heir?//
Normally birth certificate is not required. On the basis of local enquiry and on the basis of other documents like family card, school records to support you claim, certificate will be issued.
//I was told, if property is involved, we cannot apply for legal heir unless we have a suit for declaration.//
It is incorrect. It is absolutely wrong guidance.
//A suit for partition was alread filed.//
Suit for partition will divide the property and will not give legal heirship.
To prove legal heirship, legal heir certificate issued by competant authority is necessary.