My personal headcanon is that the reason Dragomas both knows how to turn into an Imperial Dragon and secured a treaty with Cathay is because he romanced a princess (or prince?) of the Imperial family while he was in Cathay and they taught their boytoy some family tricks. And maybe shared some info about draconic development while they were at it - I doubt he left a lovechild in Cathay, but whoever he was shacking up with might have had a draconic nephew or niece or something that they talked about at some point.
I think she would care, actually, if only because the tithe requirement is lower for Magisters than for Journeymen and that's more money staying in her coffers. I suspect the barrier is more that without Mathilde's fast travel options it would probably be a months-long round trip just to go to Altdorf and back, and that's without considering that she'd probably want to take a few months in her College to prep before testing (as Mathilde did herself). So it's just highly inconvenient to her current commitments/priorities. She'll probably knock it out if she ever finds herself closer to the Empire is my theory.
I think that Ulthuan can make Orbs of Sorcery because the Great Vortex directly over Ulthuan is also technically a breach in the barrier between reality and the Warp. Canonically, the tops of mountains in Ulthuan have a very thin veil between reality and the Warp because they're closer to the Great Vortex, so IMO the high elves probably have some mountaintop manufacturing site for them somewhere in Ulthuan.
I also suspect that Teclis just sent back to Ulthuan to have some Orbs magically mailed to him and refused to explain to the humans where they came from, because elves love mysterious smugness just as much as Grey Wizards. Or, y'know, canonically the main use for Orbs of Sorcery in the Empire is for Battle Altars, and the whole point of Teclis' trip was to train the humans to use magic in battle to stop the Everchosen. It would have actually made a great deal of sense for him to bring equipment for that with him that he wouldn't be able to produce locally, and I don't think there's any particular evidence that powerstones/Orbs actually are particularly volatile.