We don't know, and it's moot. These are characters from entirely different spheres of stories.

I don’t think he can adapt fast enough and in the way he’d need to before they vaporize him

How would they vaporize him?

Stopping him is not the Endless' job, they wouldn't fight him for he is no real threat to their domains. The Spectre punishes the wicked; Doomsday is not a creature of virtue and vice, only destruction.

That's why it's moot.

Can I ask, how does Death role works, because even if she does her job and not abandon it, how come some characters keep coming back, and further more in a stupid direction, doesn't mention her. So does that mean, Doomsday can escape from Death, but I hear Death can take away immortality and kill them immortals, is it because of Destiny then, he knows how the story goes and tells Death who to return, so she doesn't meet them the first time they die? I know this is too much, but it's a thought, right.

In any story not about the Endless, the writers did not take them into account. They're irrelevant in any story not their own.

The Endless are not stats sheets.

So in their comics, it explained that they literally are what they are to be called, and they do the roles and exist based on that concept, but how dependent and relevant is the concept and entity to each other?

They are personifications of intangible qualities. That is all. It doesn’t make sense because it’s a fun storytelling device. Just as any god mythos has flaws of logic because a god mythos is a human interpretation of concepts they can’t full grasp. The Endless are just another philosophical attempt at understanding what we can’t factually know.

If you are asking questions that aren’t answered in the fictional mythos, you are simply posing conjecture. There are no answers unless the writer creates them. Any in-universe answers are simply more interpretations of others.

If DC can make a story in which the Joker tricks Mr. Myxzptlk into transferring his powers into him, then it can also make a story in which Doomsday beats the crap out of the Endless and Spectre.

It's the DC Universe. Weird stuff like this happens all the time.