[CapriciousCptl]

Broadly speaking, two types of death are recognized with organ donation. Brain death, where there's no brain function at all and cardiac death, where there's no cardiopulmonary function.

Brain death in isolation generally provides the most viable organs, since it minimizes so-called "warm ischemia" time, which is the time that the organs are warm and without viable blood flow. However, sometimes patients don't meet brain death criteria strictly, or they do but the donor next of kin decides to donate after cardiac death (actually, the next of kin/family determines what the donor would have wanted and there is a strict legal/ethical precedence on what opinions count). In those cases, cardiac death is initiated by stopping life support and waiting 2-10 minutes after "death" to initiate organ harvest.

So, it's not that the heart caused death, it's just that it stopped beating, generally, due to lack of oxygen. Which means some of its cells certainly died, but by minimizing the warm ischemia time (by hooking up to a kind of life-support machine), that damage can be limited.

Patients do not have to matched strictly by age. Anatomically-speaking, body-size is the most important criterion. Obviously, matching needs to happen on antibodies/rejection and several other factors as well.