A Testator is a person who, having died, has left behind a valid Will. A person is said to have died intestate if he does not leave behind a valid Will.
A person who dies without making a Will is said to have died intestate. Even where a person has made a Will but does not state what is to be done with a particular asset, that person is said to have died intestate in relation to such asset. The Indian Succession Act, 1925 and specific laws of certain religions govern the disposal of asset of an intestate. In case of an Intestate, an Administrator may be appointed through a Letter of Administration.
A person who benefits from something, like a Will, trust etc. If you leave a particular asset to a person X after your death, under a Will, then person X is the beneficiary in respect of that asset; such a person is also referred to as a Legatee.
An heir is a person who is legally entitled to the asset of another person on that person's death. In this site and service, heir in relation to any person means the current spouse of such person and all persons lineally descended (ie sons, daughters, grandsons, grand daughters and so on) from that person. In this site and service, parents are not included as heirs.
A person predeceases another if he/she dies before that other. In the context of a Will for example, if a Beneficiary under a Will predeceases the Testator, then the bequest, in general cannot be complete unless the Testator has specified an alternate Beneficiary.