Hi there!
Wow, that's a pretty long text here, but I'll try to answer everything ~
a) Hehe. Those thought circled in your head for quite some time, right? If yes, good. Considering Dottore is manipulative and enjoys that, nothing is better than making people think about ordinary things longer than they should - and have them come up with absurd connections and unusual theories. So, Dottore basically messed with the players mind~
For the Players room, it's the same reason as a), but with something more behind it. If you would ask Dottore about it, he would tell the reason I stated above for the mirror, but I would say he actually dislikes the room for another reason. Dottore mostly has no connections to people - also he doesn't seem to view most humans as emotional and sentinent individuals. An own room changes that. A personal room is a safe space, so entering it give the feeling of entering someone's world - and I think that's what scares Dottore a little.
1. Loyal end seems to be liked by many, so I think there might be a reason hehe. As for his - kind of sudden - change of mind... The option to steal the carriage was a test - hence it was so easy. And the punishment for trying would ne the Frozen end. I originally wanted to end another choice - to poison the tea, but I figured no way the player could obtain/make/steal poison from anywhere.
The loyal end is kept pretty 'light' in terms of reason end explanation, because I wanted/will start the second game from there.
From there, the player will be able to either stay or plan their escape more detailed~ (adding that to the first game would only make the path lenght even more uneven comparing 'true spy' and 'loyal'.
2(?) I think the most 'true' end would be the loyal/obedient one, as the paths/ends are pretty similar story wise. For the true Spy end, I wanted to keep it short and pretty unsatisfying. I mean, the reason you downloaded the game surely wasn't because you wanted to initally escape from the mad Doctor, right?~ (still added it because I thought it would be kinda nice to have).
3. What Sparks His interest are unusual things/behaviour. People who carry this spark are worthy to keep around, at least that's what he believes. So your thoughts about his Initial plan to get rid of the Player and their 'wasted' escape chance is correct~
4. His relationship to the player is pretty much like you said, summed up to "obsessive" for the Immortal end and "respecting" for the other.
5. For the "Not telling the truth" Thing... Depending on the variable "letter kept/burned", If that is what you mean.
6. Yes. (I don't really need to elaborate this Fürther I guess XD Pantalone has Connections and know Dottore and his behaviour well~)
7. The actually plan of the Sages was a "Blade with two Sides". They knew the Player was a problem. Best case: the Player returns with valuable information for the Sages. Worst case: the Player's disguise would fail and *someone* would take *care* of them. So either way, it would be a win for the sages~
I also planned an actual return-to-sumeru path for the second part (which would be different than the true Spy end because the Sages never expected the Player to actually side and survive with/around the Doctor~)
Thank you for your questions and thoughts :3