Can a porcelain sink be fired again to repair surface cracks?
In theory, yes. But with any refiring, there's a chance of introducing new defects, like bubbling and so forth. The larger the piece, the more difficult it is to ensure all of it heats up uniformly. Otherwise you'll get more cracks than you started with. I have no experience with commercial services doing what you ask for on this scale (bathroom sink), but apparently some exist.