About Peter and Alexander, it is probably true that they were lovers, I have heard that more than once. So many years together, sharing friendliness, adventures and even lovers... It is not a stupid idea, from my point of view it was indeed very possible.
When Alexander was much caring for his wife than for the Tsar, Peter became very angry and jealous, so, it could be!
Of course, hikaru, there are always different points of view for every monarch... Its obvious that ours, in this particular Tsar, differ from each other. But that is normal, even better, it makes the discussion richer!