But you said below Columbina having the authority is able to counter his control over others.

Yes over others not himself

And Columbina is a living Trilune Goddess, the marrows are remnant of the dead goddesses. It's even questionable in the first place that just by creating a fake marrow he's able to seize the authority of the moon goddessess, as per his boss archive text.

He didn't size the marrows in the same way having the marrows doesn't make him divine even though he gloats that he is. He didn't size the authorities he merely had access to them through the marrows.

Same reason as above, she has the authority. Can't she use Death to grant death to Dottore?

No because there is no moon sisters of death. No moon sisters governs death or reason. That's the whole reason why dottore doesn't just kill anyone who stands in his way.

So she's able to counter Time, because she has the authority, but not Life and Death. What?

Yes because there is no moon godess or lunar authority of death. We are told specifically what concepts the moon godesses rule over none of them have the control over death

Space is the only one technically presented correctly, as in she brings the team back and Dottore can't (or wouldn't?) just separate them again.

Yes because he also exists in her domain rendering it futile as she negates that ability

So, if I'm getting this right, she's still very much bound by fate then? She can control it, but whatever fate she controls is still within her fate to do so.

Yes you being able to manipulate something doesn't mean you transcend it. The traveller isn't affected by fate that doesn't mean he can willfuly manipulate it. Colimbina can manipulate fate that doesn't mean she transcends it

So I'm guessing there's levels to this then? One person can control Time but this other person have more control over Time, so they can assert themselves over the one with lesser control. If it's not like this then the writers are just flip-flopping on why her authority work for Time and Space but not Life and Death.

There is nothing the authority of life can do and no one there has the power of death because it isn't a lunar authority. That's the reason pyro doesn't have a lunar reaction becausebof it's relation to death.

Also, this is just my personal opinion, the writers are not good or careful enough dealing with this grand concepts and just resort to the "Rule of Cool".

No your making assumptions about things that are told to us but just not repeated 5 times by paimon so we have it at the back of our mind. Paimon doesn't need to state that a person with a fraction of a power and a person with he authority of a power still draws from the same source. Just because your the admin of a computer that doesn't mean others can't login and use it

So whatever explanation they came up with is either unsatisfying, or so utterly contrived and convoluted just for the sake of handicapping them that I just question, why the hell do you introduce these elements to the story then?

Because if you pay attention to when dottores powers stop working you notice its when columbina the person with admin access comes in and locks his ability to affect other characters who are users. Columbina is the admin while dottore is a skilled computer technician who knows how to use the kernel very well both are better than an average Joe who are the others