The stigmata thingy for example
The Imaginary Space scan is likely Otto talking about base reality (Hi3 Earth) which is 4D. If not then the only other scan I can think of is Durandal saying to Kiana that they can only perceive in 3 dimensions.
The Alien Space scan is Ryusuke being 5D via the divine key he was using. Welt nullified the dimensional advantage by using his Herrscher core's connection to the Cocoon of Finality (exists above the Tree) to perceive the space Ryusuke was in and the attacks coming at him. He then decimated Ryusuke with singularity rebuild.
I don't see how this is inconsistent, it's just a hax ability and it's not like Ryusuke was on the tree.
As for Stigmata it's incredibly difficult to see what you mean by this. Here's a rundown on the basics in case you've picked up an inconsistency. I don't know how you expect me to reply, disprove or accept the story being 'inconsistent' without specifics.
True / Herrscher Stigmata - Examples are Mei and Seele. This gives them far more potential to connect with their matching core. This isn't always required, as seen with any Herrscher of Reason after Welt Joyce and Wendy.
Natural Stigmata - Created by Fire Moth, specifically Dr Mei and Mobius. This was directly inspired by Herrscher stigmata. (In the Jizo Mitama chapter of the Manga we see Stigmatas unused anywhere else, representing the divine keys made from the Previous Era Herrschers - These are blatantly their Stigmata, so we know they existed in the previous era). They can be passed on through bloodline and change people's DNA, though in the Current Era are so diluted that they need to be triggered. This makes Natural Stigmata exceptionally rare. They can still pass on things like exceptional strength even when dormant, as seen by Siegfried 1v1'ing a Honkai Beast with nothing but a metal baseball bat simply because he's a Kaslana and they're built like that.
Artificial Stigmata - Designed based on natural stigmata but due to lack of understanding they're horrid. They provide enhanced honkai resistance but decrease lifespan. People can still become zombies with Artificial Stigmata too. Himeko has this type of Stigmata.
We know every Stigmata has a related 'Stigmata Space' - Mei's stores her other consciousness and is often depicted as a white, blank space. Seele's is where her alter ego is stored and is seen in her related animated short and in the manga. We see the Kaslana Stigmata space in Chapter 31 EX and where Siegfried gets stabbed on the moon. We even see Durandal encounter the Kaslana stigmata space.
The Stigmata and Honkai are also very connected to dreams, the Honkai thinks in dreams and Vishnu, the Honkai Beast, can devour them. (This is why Theresa can devour dreams, she has Vishnu's DNA). If you want to get into what Hare is that's a whole other complicated can of worms.