Hold it right there, I can't really say much for your other points, because yes, IF they want us to do something in another Shard, they'll put something together, but on this point in particular, the English version clearly states that the Scions are literally corporeal spirits, not that the Exarch prepared vessels for them to interact with the world. The 'vessel' idea was a fan theory that people (including myself) were espousing before the expansion released, but has subsequently been debunked by the story.
The truth on Ardbert and his companions remains unclear. Did Elidibus prepare bodies for them to possess like a common Ascian, or were they, like the Scions are now, corporeal spirits? The last time this was addressed, in an interview in 2017, we were told it was left deliberately vague to allow the player to come to their own conclusion. I'm personally on the corporeal spirit side of the argument, but the vessel side is equally valid.
EDIT: (Forgot to add this before)
While we aren't given the exact mechanism by which he did it, it was G'raha who pulled us through with magic, "cutting a hole in the fabric of reality through which only the target of the spell may pass unhindered", as he put it in the 5.1 MSQ. It's a unique property to us BECAUSE someone on the other side made it so, the Scions were summoned incomplete because they were not the target and G'raha wasn't that good with the spell, at first. Yes, it is also possible that someone on another Shard may do the exact same thing to pull us through, but the ability to travel between worlds with our body is not intrinsic to us, but extrinsic.2) The Warrior of Light appears to be a unique case, in that they were able to be called to the First complete with their physical body and any belongings they possess. The means by which is this possible is never again expounded upon (only that the Scions hope to abuse it to get back via the auracite the Exarch is prepping), making it implicitly a unique property of the WoL given that this is a feat even Ardbert and his companions couldn't do.
It is implied The Tycoon was the main controlling mechanism that allowed The Crystal Tower itself to travel through time and dimensions; the time travel being what needed the most aether (See the side effects of Alexander's limited Time Travel) and thus the energies of the Tower, but opening rifts also takes quite a large amount as well, which is why Xande used the tower to open the Cloud of Darkness's rift, and let's not forget travelling through the rift apparently requires alien level technology reverse-engineered from a destroyed robot. The Exarch's portal instead seems to be born of the spell he used to pull us through, or if you think it is a more technical thing, based on the 'WoL/D-shaped' hole he made in space-time and focused on the beacon he used to lock onto us. Without the Tycoon, any time travel shenanigans by plot elements that were introduced prior in the story (optional branches of the story, but already present elements anyways) are currently not on the table, but this isn't about the time travel component so explanations on this are not of use to either of us.Not to mention that the Exarch is able to just... make a portal back to the Source within the Tower, which hasn't gone away with The Tycoon's destruction, just one that only the WoL can use.