I agree on the rust. I had it do the same thing in Houston.If this is an o-ring chain, which most likely it is, then the loose/tight sections mean some of the o-rings have failed.
Depending on OP's locale, rust by itself is not necessarily an automatic sign of impending failure. Here off the hot & extremely humid Gulf Coast, some of my chains rust just sitting in my garage, even though I'm very much on top of chain clean & lube. Even though the OEM chain still has a lot of life left, I just bought a premium replacement chain, so I don't have to deal with chain rust.
That said... since there are other signs of chain problem, OP's red dust most probably does mean trouble.