Can a sleepy character dodge?🤔
Yes.
If a character is paralyzed, but their creature is not, can the character, after skipping their turn, then ride away somewhere on the creature? (presumably yes, since the character's and pet's turns are "independent", but I'm clarifying just in case)
The character gives commands to the creature, so it also skips turns.
Is a diagonal cell considered "adjacent"?
For range 1 - no.
If you throw, for example, a pumpkin at an empty cell or a standing nearby "non-ally" and it hits Lady Moroz (or her ally), is that considered a "character's attack" (on an ally)?
It is considered if it deals direct damage.
What about the OD for this tour and for the bugurt afterwards?
They will be updated.