Doesn't make any sense
"Do you know when the Mongols ruled China?"
"Well, perhaps we can ask them!"
Even if you have a time machine at your fingertips, wouldn't you STILL have to know at least approximately 'where' (or 'when') to go to FIND the Mongols to ask them?
So if you have to know that much anyway, you have to have an easier way of obtaining such historical information, so why bother asking them, when there's clearly an easier way to get this information?
I mean, if you have (from somewhere, where exactly?) enough information to know when the Mongols even existed as an empire, why would you have to suddenly go all the way to the mongols themselves to ask questions about the time periods and eras of their conquest?
Also, would the Mongols that just started ruling China (you can't go ask the Mongols BEFORE they ruled China, because how the heck would they know?) really know exactly how long their reign will last? They can't know the future, but a time traveler should be able to.
So asking them would AT BEST give you the 'starting date' of their rule, not answer the whole 'when did they rule' question.
Furthermore, are people like Bill and Ted from San Dimas really going to be able to not only speak the Mongolian language (whatever language they spoke back then), but also understand THEIR calendar and calculation of time (even the Chinese moon calendar of the era differs greatly from the Julian calendar of modern times), AND be able to convert/translate that information to modern format..
..AND also understand Mongolian culture and everyday life to be able to understand any answer the Mongols might - - OR MIGHT NOT - - freely give them?
In what kind of situation and position, location and time can these two doofuses really ORGANICALLY and naturally ask the Mongols such a thing?
To add to all of this, just HOW suspicious would these two seem to the Mongols? They're dressed completely strangely, they speak strange language in strange voice, strange intonation, and they do strange gestures all of the time. But most importantly, even if all those problems were somehow solved;
HOW suspicious would someone be that doesn't know such a MAJOR fact about their 'great dear leader''s most recent and excellent conquest?
It makes _NO_ sense to just 'go ask the Mongols', and it makes so much more sense to acquire this information pretty much _ANY_OTHER_WAY_.
Even going to 1989 San Dimas library one day earlier or 10 years earlier would still be easier and make more sense, give more information in an immediately digestible way, etc. etc.
This part makes NO SENSE whatsoever!
But everything else is perfectly logical and cool. Beethoven would love 1980s synths.