In noting "I can't afford"; I wonder of the details of that? Certainly a Mosaic sink is a valid idea, but the issue remains in the substance of the sink. For one thing it sounds like the sink isn't porcelain at all, but cast iron, or molded Steel, coated with a fired on enamle finish. The mosaic effect, even if successful, wouldn't stop the rusting, but just hide it.

I used to know a Sculptor who made bathroom sinks, often using mosaic tile, but the sink structures were raw, unfired, until he had fabricated the design effects.

Your issue is not only effected by the fact that the subsurface is meant to be totally NON porous, but the shape of the bowl, is also working against you.

I'd probably opt for replacing the sink, and the counter, and doing your mosaic on the New counter, complimenting not only the sink, but the rest of the bath as well. Even assuming you could GRIND away the "Cooked on" surface material, you'll always have Rust to deal with, possibly to the point of leaching and staining any grout you use.

Steven Wolf
just my two "sense"