So, I watched The Higgs Field, explained - Don Lincoln and there it explains that particles are massless and it is only through their interaction with the Higg’s field that they gain mass. However, how are they “moving” through the Higg’s field? Is it through a movement in the 3rd dimension or a dimension above?
And related, does the movement through the Higg’s field generate gravitons that affect particles they interact with by “pulling” them in the opposite direction of which they were traveling?
It’s a little more complicated than that, I would recommend the following videos to get a little more insight:
PBS Space Time for a good description: https://www.youtube.com/watch?v=G0Q4UAiKacw Veritasium also has a fine more simplified description: https://www.youtube.com/watch?v=Ztc6QPNUqls
In the end you would need to do the math to really get a deeper understanding of what’s going on. There’s a lot of handwaving and analogies in popular science explanations, that isn’t the full or real story, just a way to get the gist of things.
I would also stay away from the whole concept of gravitons, our best understanding right now is that gravity is due to the shape of spacetime and thus isn’t a traditional force and has therefor no carrier. There is no such thing as a graviton as far as we know it (except for sci-fi where they are the carrier for the plot in many cases).