I don't understand Japanese, if you could provide the full translation of that scan it would be appreciated.
Magic in BC is described as something inherent in the world It also has its own laws
Being inherent to the planet/universe isn't evidence that something's conceptual or abstract, humans are inherent to planet Earth, that doesn't mean humans are conceptual entities nor abstractions.
The "laws" within this context isn't abstract nor conceptual, it's just an inherent limitation that magic seems to have, also just being bounded by a "law", with said "law" being conceptual, abstract, fundamental etc. Doesn't mean the object bounded is conceptual, abstract, fundamental etc. Without further evidence of magic existing on the same level as those laws.
as described by Klaus and was also mentioned in the databook. Lucius also describes Asta as a defect of the world for not having magic , and antimagic like something that goes against reason
Again, nothing about this proves Conceptual Manipulation. Asta defying "reason" with his Anti-Magic isn't him actually defying the concept of reason itself, what Lucius means by "defying" reason is the fact he was born without magic, which when the natural law/reason of the world is that every human is born with magic, Asta having no magic, and instead having Anti-Magic, which is antithetical to magic, would "defy" the reasoning of the world in which all humans are born with magic.
Moris also hints that with his magic that he can affect at the conceptual level he could also affect other people's magic.
Effecting something with Conceptual Manipulation doesn't mean the object in question being affected is Conceptual in nature, Morris's Conceptual Manipulation is most likely affecting the "concept" of that person's magic to directly change how the "physical" expression of that concept acts, rather then magic being a "concept" within itself. Especially when Magic is shown and described in physical terms rather than something abstract or conceptual.
And for the case of type 2 information, I'm still not sure but the knowledge/mind in BC is composed of shelves with books as shown by Lolopechika What do you think about this ? With a better explanation and with these scans is it possible to make a CRT to confirm magic as a type 2 concept and mind as type 2 information as well?
That just seems like Information Manipulation (Type 1) from what i'm seeing, it seems like she inherent'd a specific ability which allows her to read through the vast quantity of information and experiences of the previous princesses.
After reading through everything you've posted, no, i don't believe you have enough information to argue for Conceptual Manipulation (Type 2) and Information Manipulation (Type 2), regardless of how good your rhetoric is. It just isn't enough evidence imo, you could ask these more knowledgeable members on both Black Clover and CM/IM to see what their opinions are.
Black Clover:
@Arnoldstone18,
@CloverDragon03
CM/IM:
@DontTalkDT,
@Everything12,
@Theglassman12