rusty stains showing through a newly dried spackle
You have a leak - that's what causes moist drywall in virtually all cases. The rust is presumably coming from drywall nails/screws or other nails or steel/iron in the wall. Without fixing the leak first, no repair will last. Once you get the leak fixed you can coat the wall with a "stain-blocking primer" (often shellac based) to stop the rust stains from bleeding through the paint.