If available, the CLR mentioned by a couple of people might be one of the better things to try on the stains described. Other "commercial" products that might be available are commonly sold under the brand(?) name "Naval Jelly," although it comes in two different kinds, one of which is specifically for iron rust and the other for "everything else." (If there's a boat yard nearby, those guys are always fighting corrosion and rust. They might have something(?))

Oxalic acid is commonly used for "cleaning" both porcelains and textiles in industrial settings; but you should be aware that it is not just corrosive, it is also a potent nerve toxin. You should use extreme caution in using it in any "makeshift" manner - especially in combination with "other ingredients."

The porcelain on typical tubs is pretty thick, and hard enough that you're not likely to "sand through it," although the shine on new porcelain comes mostly from the soft glass that "floats" out of the mix during firing. This glaze layer is usually quite thin, and it may, or may not, form a continuous surface film, but in a new appliance it should completely coat the underlying "ceramic" material. Once you wear - or sand - through the glaze layer and expose the underlying "white stuff," the tub will be somewhat more susceptible to new stains, and a little harder to keep clean, since the "white stuff" has a tendency to be at least slightly porous.

If the tub is old enough to have a "penetrating" rust stain, it's likely the glaze is already broken; and it probably is not worth worrying too much about trying to protect it. Most of those "don't evers" that the porcelain people feed offer you are based on not damaging an intact glaze layer, so if the tub is an older one you can use your own judgement about which of them are still applicable.

Because of the porosity of the white stuff, you are not likely to sand a "major stain" off without reaching the iron/steel underneath, but you might make it if it's just "in the surface."

John