Stained Plaster - Waterproof primer before or after patching
There's no reason to prime in between layers of plaster and patching compound. Just remove any peeling paint or loose plaster and patch with new joint compound. Once the new stuff dries fully, sand it smooth, clean, prime, and paint. A decent stain-blocking primer like Kilz will do fine with an old water stain, but if you have more insidious stains (e.g. oil, knotty wood) you can use a shellac-based stain blocker.

If other patched areas are bubbling, those are signs of recent leaks or moisture. To stop those, you need to resolve the moisture issue. Until that's fixed your walls will continue to fail (and you'll be at risk of more severe damage in your wall structure, electrical, etc.).