Those look pretty simple.
You can get yacht rope at a marine supply or boating store. Also, some of the big feed/tack/hardware stores carry it, as well. There are probably a lot of online suppliers, as well.
It looks like, on those, they just burned the ends to seal them and keep the rope from fraying. You can do that with a match or a lighter. There is also a tool, the name of which escapes me right now, that has one end that grips the rope like Chinese thumb cuffs and a pointed awl on the other end that you use to thread the rope back into itself to make a smooth and very strong end.
I am not a fan of snaps on any reins other than romels with chains because I don’t like jangling on the bit when I’m handling my reins as much as I do when working a horse in a snaffle, but that’s personal preference. When I’ve set up similar reins, I just put the slobber straps through the bit rings to avoid using snaps.
You can probably find quite a bit of information online. I think some people call them “sport reins” as opposed to a mecate rein that has a tail used as a lead. Length is your personal preference depending on how you ride. Reins long enough to mosey down the trail, loose and relaxed, would get in your way if you were actually trying to rope or run barrels.