Do string instruments really create standing waves or not? I have seen similar questions regarding this but containing answers that somewhat disagree with each other which makes it hard for me to understand this.
My question is mainly about when plucking a string instrument at the end side of it, not in the middle. From several slowmotion videos, including this one and this one, I can see that this creates a single propagating wave that reflects back and forth. 
If there is no periodic plucking, there is no way that this single propagating wave would interfere with itself to produce standing waves and thus harmonics. And yet, I keep reading that plucking a string instrument (once) would produce (a mixture of) harmonics. How is this possible with a single propagating wave that can not interfere with itself? 
Are there other conditions, other than interfering propagating waves, that produce harmonics?
 A: Anything happening on a guitar string can be always written as a superposition of standing waves of different harmonic frequencies. Even the initial motion, which is clearly bouncing back and forth, can be written in this way. (This should not be surprising. After all, standing waves themselves are written by combining solutions that only propagate in one direction. I'm just saying we can undo that.) So technically the answer to your question is just, yes, essentially by definition.
There's another sense in which the answer is yes. As the oscillation continues, higher frequency standing waves decay due to dissipation, leaving behind a simple combination of a few, low-frequency standing waves. So even though the solution is always formally a combination of standing waves, as time goes on, the guitar's behavior will look more and more like the examples of simple standing waves that you find in your textbooks. You can see this starting to happen towards the end of the first video you linked.
