The stars, Moon and Sun (singular) are exactly where they should be. Right after Christmas, the Moon indeed set in the west-southwest. Two weeks later (a matter of days ago), it set in the west-northwest approximately at sunrise. This is how the Moon has behaved for as long as humans have observed it. The cause is simply the orbital dynamics of the Earth-Moon system.
You can download any planetarium software (like Stellarium) and find where any object will be at any given time, relative to your location.
she noticed the changes in speed of the moon during the night
I don't even know what this means. How did she make this determination? Who else noticed? If the Moon changed speed, why is it still rising and setting right on schedule? Doesn't make any sense.
Over the course of a month, the Moon will be visible for different amounts of time. On December 26, the Moon was above the horizon for roughly 10.5 hours. On January 9, it was closer to 11 hours. Later this month there will be roughly 14.5 hours between moonrise and moonset.
Ihave read many stories about people who have seen changes in the stars, moon, and suns positions over a very short period of time (even just hours)..
Everything in the sky appears to move, because Earth rotates on its axis. Local objects like the Moon and planets are close enough for us to notice the consequences of their own movement. Other objects are so far away that they are referred to as the "fixed" background, even though they aren't fixed at all, but things still change position from our perspective due to our planet's own motion. If you are truly an "avid night sky watcher," I'm confused as to why this is such a mystery to you. Further, I'll give you million to one odds that none of these people allegedly noticing oddities are astronomers. If anything truly were out of the ordinary, why haven't any astronomers noticed?