If there's hard water buildup you can use muriatic (swimming pool) acid, diluted to about 20% (add 1 part acid to about 5 parts water). I've used it straight and it works well and quickly. Just don't let it sit on chrome for more than a few seconds or it'lll blue/black it.
For rust staining something with phosphoric acid should get it off the porcelin but may have to sit an hour or more to bleach it out. Bleach may do some but not against hard water, grime or rust. If it's dulled and most likely is, use a sink cleaner called Zud. It's very abrasive so only scrub as long as you have to. White and slightly dull looks better than dingy and a sheen from glossed over grime. You could then used some rubbing compounds and lots of elbow grease to shine it back up. Not that Zud will make it dull. Just use it sparingly. Cool find!
