what you have is a 3 ways wiring circuit. It’s a little more complicated than just one switch and light so I refer you to this post for more info.
as for your second question about the circuit with no neutral. there are couple of ways to deal with this.
you mentioned about a neutral in the same box but possible not the same circuit and didn’t work. This actually is not true. Neutral will still work even on another circuit. Just that’s it’s against code, overload (fire hazard) and GFCI issue. So stay away for your own good. I would say you need to read a little more about basic home wiring before going further so you can be comfortable dealing with this since HA is an addiction and pretty sure you will change more switches later.
This post has the same problem.