Yes, it'll work, at least in my experience. Officially, though, a C41 fixer should be near-pH neutral; I think they're typically pH6.5-ish. This is allegedly to ensure the dyes adopt the hue as designed. However, as far as I know, the dyes in modern C41 films are pretty stable across a broad pH range, so the use of an acid B&W fixer probably won't make much of a difference.
Don't know and I doubt any C41 is qualified for an alkaline fixer since C41 fixer has been pH6.5 for a loooong time. I doubt Kodak would bother qualifying it for anything else to be honest.
Yes, I think there are a few pH neutral fixers on the market from niche players. Should work fine with C41 film.
I was told by someone decades ago that C-41 fixer was good for B&W but not the other way around. At one time Agfa sold a universal fixer E-6, C41 and B&W. I used to order it from Unique photo. One time the box was damaged by UPS and it leaked from one end of the truck to the other. I refused delivery on that one. I bet it fixed their truck.