Did the parchment contain a letter or informal message? Yes
Did Princess Aouda sign or leave any indication that she wrote the letter/message on the parchment?Only by way of indication that it was written by the sole occupant of that room,otherwise they would have known what name to put on the gravestone

 

Was Princess Aouda directing the message to the innkeeper or trying to tell the innkeeper something? Oh yes

In the note, did she mention any of the following:
Genghis Khan?No
Her fall?I am not sure what you mean by "Her fall" so No
The eternal flame?Yes

By "Her fall" I meant the point where she tripped and the innkeeper caught her from falling.
In which case Yes

Did the princess tell the innkeeper to hang himself, directly (words that say hang yourself or something like that) or indirectly (conditions that were met so he had to hang himself/hidden message (encoded))?
No she neither directly nor indirectly told him to hang himself. Nor was his name King Louie (bad pun,King of the swingers)

I would like to ask a question that would require more then a yes or no answer, but I believe it has nothing to do with solving the riddle, just the storyline.
What became of the innkeeper's body?
They covered it in clay , baked it and then made a golem out of it by writing the answer to this riddle on parchment and placing it in its mouth........ Nah only kidding they cremated it

Hmm... there's a lot of cremation in this riddle - one wouldn't dare to ask what will happen to the horses when they die - and though nothing related to religion, there's indeed a lot turning to ashes...
Dead horses are appointed to be bureaucrats, The Khan found that they cost nothing to employ,didn't take bribes and didn't interfere with what was working perfectly well.
Then, if it is still a fact the innkeeper's dead is related to what he read on the note, did what he read (YES) like 'trigger' a plan the man was carrying in his head before, or (NO) would he never have taken his life if he hadn't read it?
NO would he never have taken his life if he hadn't read it?

How the innkeeper came to hang himself...

Zach's theory: SORCERY! Princess Aouda was in fact to be married to Genghis Khan's son next day. As tradition requires she had to spend the night before the wedding without her future husband. So she went to a party with some friends. At the party they played a song about an 'eternal flame' (successfully covered by The Bangles many years after), and she met this old woman who told her about the eternal flames of Alexander the Great. The woman told her that she should not be fooled by any guy pretending to have the 'eternal flame', as probably he was just another Viagra addict, and that the real flames where nothing more than those burning in a fire pit, guarded by an innkeeper and his dog at a town nearby. It was said the flames could give prophesy power to the right person who looks into them. Curious about the future lying ahead with her new marriage, and also about finding out about the flames, she went to the hotel the same night, guided by a short road map the old woman wrote her. When she was alone in her room, she stared so long into the flames - waiting for some 'message' of prophesy to pop out - that she became blind... While hoping her loss of sight was only temporarily, she went to sleep, not aware the innkeeper's dog was sleeping on the bed after a long day of watching the stables. Of course the dog didn't like her company on the bed and it took a while for her to realize the gowning of the dog was a little heavy to sound like the snoring of her future husband that she dreamed about had snipped into her bed during the night. Especially when the barking began, she was sure about nothing less as a monster had invaded her room and - while still blind - she jumped out of bed... right into the fire pit... Naked women and fire pits don't really match when they are to close to each other. She turned to ashes. While the room filled with smoke, the dog started to howl - solving the mystery who created the smoke detectors they sell nowadays - and the innkeeper rushed in the room. When he saw what happened, he also found the note on the table, containing the road map. He recognized the old women's writing to be his mother's, who disappeared many years ago as a supposed victim of a local serial killer who was in prison now. When the serial killer was condemned, his possessions were sold and the money went to the family of the victims. The innkeeper bought the hotel with the money he received for the murder on his mother, but now he knew his mother was still alive, he feared he would lose the hotel again... and the stables making part of it. While thinking about this, he stared into the flames of the fire pit... and got a vision: he saw how his hotel was sold and became a wellness centre, with a sauna on top of the fire pit. When the owner was found dead one day - drown in the jacuzzi - the wellness became a restaurant, where the eternal flame came in handy for non-stop cooking in the kitchen. But that was nothing that really annoyed the innkeeper. His biggest concern was this restaurant would be the first to serve... horse meat to the customers. The image of his horses being killed and cooked terrorized him, and he quickly ran to the stables. Once there, he jumped on his most expensive horse, and wanted to ride away with it to save it. While riding trough the stables to the exit, he got caught by a rope and hang himself... It is said - but never been checked properly - his spirit would travel the world to find someone to post a riddle and solve the mystery of his dead once and for all...
What can I say, I am astounded! You are absolutely...................Wrong

LOL @Zach

Did the woman die an accidental death?
No it was not accidental

@Zach Good story
I haven't gotten any ideas yet, but I think the message is key to solving this riddle.
In the message, did the princess mention anything about hanging yourself?
What's with this hanging me? I am not the innkeeper! No there was nothing in the message about the innkeeper hanging himself.

Was the innkeeper scared into hanging himself?
A difficult question to answer Tattle, but on balance I would say no, he made a rational decision to end his life

Did the message include anything related to killing himself?
If yes, was there two (or more) choices and the innkeeper chose the choice which meant death?
No, nothing in the message indicated that the innkeeper should kill himself, the princess would not so interfere with someone elses karma

Was the innkeeper's emotion the cause of his death after reading the message?
No, it was a rational decision

See?

Anyway, if the innkeeper didn't hang himself by accident while escaping with the most expensive horse, then did he do it by free will to escape from something?
Yes that is correct

So, he used rational free will to hang himself by escaping the eternal flame?
No eternal flames are fixed in one place, they are not pyroclastic flows or roaming St Elmo's fires(corposants), they are not hypnotic inducers of suicide nor do they release any unusual gases, they are just very pleasant cerulean blue flames ( at least those that I have seen are). No I am still not going to tell where you can find one

Hmm, well i wasnt wanting to know where one was, being that the last two people that were near it died.
I want to know did he rationally hang himself on account of the eternal flame?
No, his death had nothing to do with the eternal flame.