About the apoptosis mechanisms in a cell
Not at all. In order to self destruct, you don't need to disable all necessary functions, you just need to disable one. That's why the functions are called "essential". To take a very simple example, in every movie you've seen where the self destruct has been activated, that self destruct mechanism was almost certainly a bomb that blew the ship/installation/planet or whatever up. The self destruct did not go around disabling individual processes, it just activated a bomb and destroyed everything.

Apoptosis is quite similar. While there are many essential processes in a cell whose failure can activate apoptosis, the mechanism of apoptosis itself usually involves the straightforward destruction (lysis) of the cell. Simply put, the cell digests itself, breaking down its various constituent parts and, finally, destroying the cell membrane and breaking up the cell itself. For a summary see this Wikipedia page or here.

Briefly, when apoptosis is triggered, the caspase cascade is initialized which results in the breakdown of various proteins in the cell and, finally, in cell lysis. It really is analogous to setting of the bomb that destroys the facility of the bad guys.